Question 1

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent.
-In how many ways can you get a bunch of three history books and seven novels to give to a friend?

Accepted Answer

The answer of suppose you have 30 books (15 novels,...

Question 2

let A be the set of all bit strings of length 10.
-How many bit strings of length 10 have exactly six 0's?

Accepted Answer

The answer of let A be the set of all...

Question 3

let A be the set of all bit strings of length 10.
-How many bit strings of length 10 have equal numbers of 0's and 1's?

Accepted Answer

The answer of let A be the set of all...

Question 4

let A be the set of all bit strings of length 10.
-How many bit strings of length 10 have more 0's than 1's?

Accepted Answer

The answer of let A be the set of all...

Question 5

a club with 20 women and 17 men needs to form a committee of size six.
-How many committees are possible if the committee must have three women and three men?

Accepted Answer

The answer of a club with 20 women and 17...

Question 6

A class consists of 20 sophomores and 15 freshmen. The class needs to form a committee of size ﬁve. (a) How many committees are possible? (b) How many committees are possible if the committee must have three sophomores and two freshmen?

Accepted Answer

The answer of A class consists of 20 sophomores and...

Question 7

Suppose $| A |$  =10  and $| B |$  =4 . Find the number of  1-1  functions $f : A \rightarrow B$

Accepted Answer

The answer of Suppose $| A |$  =10 ...

Question 8

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent.
-In how many ways can you put the 30 books in a row on a shelf?

Accepted Answer

The answer of suppose you have 30 books (15 novels,...

Question 9

A club with 20 women and 17 men needs to choose three diﬀerent members to be president, vice president,and treasurer.
(a) In how many ways is this possible? 
(b) In how many ways is this possible if women will be chosen as president and vice president and a man as treasurer?

Accepted Answer

The answer of A club with 20 women and 17...

Question 10

A class consists of 20 sophomores and 15 freshmen. The club needs to choose four diﬀerent members to be president, vice president, secretary, and treasurer. 
(a) In how many ways is this possible? 
(b) In how many ways is this possible if sophomores will be chosen as president and treasurer and freshmen as vice president and secretary?

Accepted Answer

The answer of A class consists of 20 sophomores and...

Question 11

a club with 20 women and 17 men needs to form a committee of size six.
-How many committees are possible if the committee must consist of all women or all men?

Accepted Answer

The answer of a club with 20 women and 17...

Question 12

Suppose $A$ =4  and |$B$| =10 . Find the number of functions $f : A \rightarrow B$

Accepted Answer

The answer of Suppose $A$ =4  and |$B$| =10...

Question 13

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent.
-In how many ways can you put the 30 books in a row on a shelf if the ﬁve math books are to be grouped together, but there are no restrictions on the placement of the other books?

Accepted Answer

The answer of suppose you have 30 books (15 novels,...

Question 14

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483
are strings in A.
-How many strings in A begin with 774?

Accepted Answer

The answer of let A be the set of all...

Question 15

Suppose |$A$|  =4  and |$B$|  =10 . Find the number of 1-1 functions $f : A \rightarrow B$

Accepted Answer

The answer of Suppose |$A$|  =4  and |$B$|...

Question 16

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent.
-In how many ways can you get a bunch of four books to give to a friend?

Accepted Answer

The answer of suppose you have 30 books (15 novels,...

Question 17

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent.
-In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

Accepted Answer

The answer of suppose you have 30 books (15 novels,...

Question 18

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483
are strings in A.
-Find |A|.

Accepted Answer

The answer of let A be the set of all...

Question 19

a club with 20 women and 17 men needs to form a committee of size six.
-How many committees are possible?

Accepted Answer

The answer of a club with 20 women and 17...

Question 20

a club with 20 women and 17 men needs to form a committee of size six.
-How many committees are possible if the committee must have at least two men?

Accepted Answer

The answer of a club with 20 women and 17...

Quiz 6: A: Counting

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you get a bunch of three history books and seven novels to give to a friend?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have exactly six 0's?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have equal numbers of 0's and 1's?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have more 0's than 1's?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must have three women and three men?

A class consists of 20 sophomores and 15 freshmen. The class needs to form a committee of size ﬁve. (a) How many committees are possible? (b) How many committees are possible if the committee must have three sophomores and two freshmen?

Suppose $| A |$ =10 and $| B |$ =4 . Find the number of 1-1 functions $f : A \rightarrow B$

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf?

A club with 20 women and 17 men needs to choose three diﬀerent members to be president, vice president,and treasurer. (a) In how many ways is this possible? (b) In how many ways is this possible if women will be chosen as president and vice president and a man as treasurer?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must consist of all women or all men?

Suppose $A$ =4 and | $B$ | =10 . Find the number of functions $f : A \rightarrow B$

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf if the ﬁve math books are to be grouped together, but there are no restrictions on the placement of the other books?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A begin with 774?

Suppose | $A$ | =4 and | $B$ | =10 . Find the number of 1-1 functions $f : A \rightarrow B$

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you get a bunch of four books to give to a friend?

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -Find |A|.

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must have at least two men?

Quiz 6: A: Counting

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you get a bunch of three history books and seven novels to give to a friend?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have exactly six 0's?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have equal numbers of 0's and 1's?

let A be the set of all bit strings of length 10. -How many bit strings of length 10 have more 0's than 1's?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must have three women and three men?

A class consists of 20 sophomores and 15 freshmen. The class needs to form a committee of size ﬁve. (a) How many committees are possible? (b) How many committees are possible if the committee must have three sophomores and two freshmen?

Suppose ∣A∣| A |∣A∣ =10 and ∣B∣| B |∣B∣ =4 . Find the number of 1-1 functions f:A→Bf : A \rightarrow Bf:A→B

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf?

A club with 20 women and 17 men needs to choose three diﬀerent members to be president, vice president,and treasurer. (a) In how many ways is this possible? (b) In how many ways is this possible if women will be chosen as president and vice president and a man as treasurer?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must consist of all women or all men?

Suppose AAA =4 and | BBB | =10 . Find the number of functions f:A→Bf : A \rightarrow Bf:A→B

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf if the ﬁve math books are to be grouped together, but there are no restrictions on the placement of the other books?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A begin with 774?

Suppose | AAA | =4 and | BBB | =10 . Find the number of 1-1 functions f:A→Bf : A \rightarrow Bf:A→B

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you get a bunch of four books to give to a friend?

suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are diﬀerent. -In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -Find |A|.

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible?

a club with 20 women and 17 men needs to form a committee of size six. -How many committees are possible if the committee must have at least two men?

Suppose $| A |$ =10 and $| B |$ =4 . Find the number of 1-1 functions $f : A \rightarrow B$

Suppose $A$ =4 and | $B$ | =10 . Find the number of functions $f : A \rightarrow B$

Suppose | $A$ | =4 and | $B$ | =10 . Find the number of 1-1 functions $f : A \rightarrow B$