Question 1

Evaluate $P ( 7,5 )$ .
​ $P ( 7,5 )$ __________

Accepted Answer

The answer of Evaluate $P ( 7,5 )$ .
​ \(P...

Question 2

Evaluate $P ( 6,2 )$ .
​ $P ( 6,2 )$ __________

Accepted Answer

The answer of Evaluate $P ( 6,2 )$ .
​ \(P...

Question 3

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

Accepted Answer

The answer of In how many ways can a 5-card...

Question 4

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

Accepted Answer

The answer of How many five-letter sequences are possible that...

Question 5

A bag contains 3 red marbles, 5 blue marbles, 3 yellow marbles, and 2 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

Accepted Answer

The answer of A bag contains 3 red marbles, 5...

Question 6

Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible  ?

Accepted Answer

For the true/false questions, there are 2 possibilities for each question, making it $2^{11}$ possibilities. For the multiple choice questions, there are 4 possibilities for each question, making it $4^5$ possibilities. The total number of possible answer sheets is the product of these two, which is $2^{11} \times 4^5 = 2,048 \times 1,024 = 2,097,152$.

Question 7

Evaluate $\frac { 4 ! } { 1 ! }$ .
​ $\frac { 4 ! } { 1 ! } =$ __________

Accepted Answer

The answer of Evaluate \(\frac { 4 ! } {...

Question 8

Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch four movies selected at random from the list. How many sets of four movies are possible    $$\begin{array} { | c | c | } 
\hline \text { Name } & \text { Revenue (\$ million) } \
\hline \text { The Grudge } & \$ 9.24 \
\hline \text { Ray } & \$ 6.54 \
\hline \text { The Forgotten } & \$ 6.01 \
\hline \text { Friday Night Lights } & \$ 5.99 \
\hline \text { Cellular } & \$ 5.85 \
\hline \text { Shall We Dance } & \$ 5.82 \
\hline \text { The Village } & \$ 5.58 \
\hline \text { AVP: Alien Vs. Predator } & \$ 5.46 \
\hline \text { Catwoman } & \$ 5.10 \
\hline \text { Sky Captain and the World of } \
\text { Tomorrow } & \$ 5.09 \
\hline
\end{array}$$

Accepted Answer

The total number of movies listed is 10. The number of ways to select 4 movies out of 10 is calculated using the combination formula, which is $C(n, k) = \frac{n!}{k!(n-k)!}$. Substituting $n=10$ and $k=4$, we get $C(10, 4) = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$. Therefore, there are 210 possible sets of four movies.

Question 9

Evaluate $C ( 3,1 )$ .
​ $C ( 3,1 ) =$ __________

Accepted Answer

The answer of Evaluate $C ( 3,1 )$ .
​ \(C...

Question 10

A computer byte consists of 8 bits, each bit being either a 0 or a 1. If characters are represented using a code that uses 2 bytes for each character, how many characters can be represented  ?

Accepted Answer

One byte consists of 8 bits, therefore 2 bytes represent 2 x 8 = 16 bits.

Each bit can represent either 0 or 1. Therefore, the number of possible combinations of 16 bits is 2^16.

Hence, the number of characters that can be represented is 2^16 = 65,536.

Therefore, the correct answer is C.

Question 11

The "Dogs of the Dow" refer to the stocks listed on the Dow with the highest dividend yield. The table shows the top ten stocks of the "Dogs of the Dow" list in February, 2005. You decide to make a small portfolio consisting of a collection of six of the top ten Dogs of the Dow. $$\begin{array} { | c | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Price } & \text { Yield } \
\hline \text { SBC } & \begin{array} { c } 
\text { SBC } \
\text { Communications }
\end{array} & 23.62 & 5.46 \% \
\hline \text { GM } & \text { General Motors } & 36.64 & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 28.02 & 5.42 \% \
\hline \text { MO } & \text { Altria } & 63.20 & 4.62 \% \
\hline \text { VZ } & \text { Verizon } & 35.68 & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 37.00 & 3.68 \% \
\hline \text { C } & \text { Citigroup } & 48.38 & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 24.35 & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 47.23 & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 35.75 & 2.46 \% \
\hline
\end{array}$$  
How many portfolios are possible ?
__________ portfolios
How many of these portfolios contain SBC but not MO ?
__________ portfolios
How many of these portfolios contain at most one stock priced above $40 ?
__________ portfolios

Accepted Answer

The answer of  The "Dogs of the Dow" refer...

Question 12

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A).
​
__________ hands

Accepted Answer

The answer of A poker hand consists of five cards...

Question 13

A bag contains 5 red marbles, 4 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many possible sets of three marbles are there

Accepted Answer

The answer of A bag contains 5 red marbles, 4...

Question 14

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

Accepted Answer

The answer of A bag contains 3 red marbles, 6...

Question 15

How many eight-letter sequences are possible that use the letters p, r, o, p, e, r, t, y

Accepted Answer

The answer of How many eight-letter sequences are possible that...

Question 16

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations).
​
__________ hands

Accepted Answer

The answer of A poker hand consists of five cards...

Question 17

Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch six movies selected at random from the list.
?? $$\begin{array} { | c | c | } 
\hline \text { Name } & \text { Revenue ( } \text { ( million) } \
\hline \text { The Grudge } & \$ 9.24 \
\hline \text { Ray } & \$ 6.54 \
\hline \text { The Forgotten } & \$ 6.01 \
\hline \text { Friday Night Lights } & \$ 5.99 \
\hline \text { Cellular } & \$ 5.85 \
\hline \text { Shall We Dance } & \$ 5.82 \
\hline \text { The Village } & \$ 5.58 \
\hline \text { AVP: Alien Vs. Predator } & \$ 5.46 \
\hline \text { Catwoman } & \$ 5.10 \
\hline \begin{array} { c } 
\text { Sky Captain and the World of } \
\text { Tomorrow }
\end{array} & \$ 5.09 \
\hline
\end{array}$$ 
a. How many sets of six movies are possible ? 
__________ sets
b. Your best friends, the Lara twins, refuse to see "Shall We Dance" on the grounds that it is "for girliemen" and also insists that at least one of "Alien Vs. Predator" or "Sky Captain" be among the movies selected. How many of the possible groups of six will satisfy the twins ? 
__________ groups
c. Comparing the answers in parts (a) and (b), would you say the Lara twins are more likely than not to be satisfied with your random selection ? 
__________ (yes or no )

Accepted Answer

The answer of Rather than study for math, you and...

Question 18

Evaluate $C ( 8,3 )$ .
​ $C ( 8,3 )$ __________

Accepted Answer

The answer of Evaluate $C ( 8,3 )$ .
​ \(C...

Question 19

Find the indicated value.
​
7!

Accepted Answer

The answer of Find the indicated value.
​
7!...

Question 20

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes  ?
__________ handshakes

Accepted Answer

The answer of If 10 persons meet at a reunion...

Quiz 7: Sets and Counting

Evaluate $P ( 7,5 )$ . $P ( 7,5 )$ __________

Evaluate $P ( 6,2 )$ . $P ( 6,2 )$ __________

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

A bag contains 3 red marbles, 5 blue marbles, 3 yellow marbles, and 2 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible ?

Evaluate $\frac { 4 ! } { 1 ! }$ . $\frac { 4 ! } { 1 ! } =$ __________

Evaluate $C ( 3,1 )$ . $C ( 3,1 ) =$ __________

A computer byte consists of 8 bits, each bit being either a 0 or a 1. If characters are represented using a code that uses 2 bytes for each character, how many characters can be represented ?

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A). __________ hands

A bag contains 5 red marbles, 4 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many possible sets of three marbles are there

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

How many eight-letter sequences are possible that use the letters p, r, o, p, e, r, t, y

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). __________ hands

Evaluate $C ( 8,3 )$ . $C ( 8,3 )$ __________

Find the indicated value. 7!

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes ? __________ handshakes

Quiz 7: Sets and Counting

Evaluate P(7,5)P ( 7,5 )P(7,5) . ​ P(7,5)P ( 7,5 )P(7,5) __________

Evaluate P(6,2)P ( 6,2 )P(6,2) . ​ P(6,2)P ( 6,2 )P(6,2) __________

In how many ways can a 5-card hand containing 4 kings and 1 queen be dealt from a deck of 52 cards

How many five-letter sequences are possible that use the letters b, l, a, c, k once each

A bag contains 3 red marbles, 5 blue marbles, 3 yellow marbles, and 2 lavender marbles. How many sets of 3 marbles include none of the yellow marbles

Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible ?

Evaluate 4!1!\frac { 4 ! } { 1 ! }1!4!​ . ​ 4!1!=\frac { 4 ! } { 1 ! } =1!4!​= __________

Evaluate C(3,1)C ( 3,1 )C(3,1) . ​ C(3,1)=C ( 3,1 ) =C(3,1)= __________

A computer byte consists of 8 bits, each bit being either a 0 or a 1. If characters are represented using a code that uses 2 bytes for each character, how many characters can be represented ?

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A). ​ __________ hands

A bag contains 5 red marbles, 4 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many possible sets of three marbles are there

A bag contains 3 red marbles, 6 blue marbles, 2 yellow marbles, and 2 lavender marbles. How many sets of 4 marbles include at most one of the yellow marbles

How many eight-letter sequences are possible that use the letters p, r, o, p, e, r, t, y

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). ​ __________ hands

Evaluate C(8,3)C ( 8,3 )C(8,3) . ​ C(8,3)C ( 8,3 )C(8,3) __________

Find the indicated value. ​ 7!

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes ? __________ handshakes

Evaluate $P ( 7,5 )$ . $P ( 7,5 )$ __________

Evaluate $P ( 6,2 )$ . $P ( 6,2 )$ __________

Evaluate $\frac { 4 ! } { 1 ! }$ . $\frac { 4 ! } { 1 ! } =$ __________

Evaluate $C ( 3,1 )$ . $C ( 3,1 ) =$ __________

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of the flush (five cards all of the same suit, but not consecutive denominations: A, 2, 3, 4, 5 up through 10, J, Q, K, A). __________ hands

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). __________ hands

Evaluate $C ( 8,3 )$ . $C ( 8,3 )$ __________

Find the indicated value. 7!