Question 1

You have 20 cards and 12 envelopes (labeled 1, 2, . . . , 12). In how many ways can you put the 20 cards into
the envelopes if
(a) the cards are distinct.
(b) the cards are identical.
(c) the cards are identical and no envelope can be left empty.

Accepted Answer

The answer of You have 20 cards and 12 envelopes...

Question 2

Find the next largest permutation in lexicographic order after 1324.

Accepted Answer

The answer of Find the next largest permutation in lexicographic...

Question 3

Find the next largest permutation in lexicographic order after 6714235.

Accepted Answer

The answer of Find the next largest permutation in lexicographic...

Question 4

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40
orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical,
-How many handfuls of 15 are possible with at least two pieces of each ﬂavor?

Accepted Answer

The answer of assume that you have a bowl containing...

Question 5

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40
orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical,
-How many handfuls of 15 are possible with at least three pieces of each ﬂavor?

Accepted Answer

The answer of assume that you have a bowl containing...

Question 6

assume that you have 50 pennies and three jars, labeled A, B, and
-In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar
must have at least two pennies put into it?

Accepted Answer

The answer of assume that you have 50 pennies and...

Question 7

Find the next four largest 4-combinations of the set {1, 2, 3, 4, 5, 6, 7, 8} after {1, 2, 3, 5}.

Accepted Answer

The answer of Find the next four largest 4-combinations of...

Question 8

If the permutations of  1,2,3,4,5,6  are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation immediately before  534126 .

Accepted Answer

The answer of If the permutations of  1,2,3,4,5,6 ...

Question 9

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40
orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical,
-How many handfuls of 15 are possible with at least one piece of each ﬂavor?

Accepted Answer

The answer of assume that you have a bowl containing...

Question 10

If the permutations of  1,2,3,4,5,6  are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation in position #483.

Accepted Answer

The answer of If the permutations of  1,2,3,4,5,6 ...

Question 11

assume that you have 50 pennies and three jars, labeled A, B, and
-In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar
must have an even number of pennies put into it?

Accepted Answer

The answer of assume that you have 50 pennies and...

Question 12

If the permutations of  1,2,3,4,5,6  are written in lexicographic order, with 123456 in position # 1,123465 in position #2, etc., find the permutation immediately after 246531 .

Accepted Answer

The answer of If the permutations of  1,2,3,4,5,6 ...

Question 13

You have a pile of 20 identical blank cards. On each card you draw a circle, a plus, or a square. How many
piles of 20 cards are possible?

Accepted Answer

The answer of You have a pile of 20 identical...

Question 14

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40
orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical,
-How many handfuls of 15 are possible?

Accepted Answer

The answer of assume that you have a bowl containing...

Question 15

Find the next largest permutation in lexicographic order after 52143.

Accepted Answer

The answer of Find the next largest permutation in lexicographic...

Question 16

Find the next largest permutation in lexicographic order after 3254781.

Accepted Answer

The answer of Find the next largest permutation in lexicographic...

Quiz 6: Counting

You have 20 cards and 12 envelopes (labeled 1, 2, . . . , 12). In how many ways can you put the 20 cards into the envelopes if (a) the cards are distinct. (b) the cards are identical. (c) the cards are identical and no envelope can be left empty.

Find the next largest permutation in lexicographic order after 1324.

Find the next largest permutation in lexicographic order after 6714235.

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical, -How many handfuls of 15 are possible with at least two pieces of each ﬂavor?

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical, -How many handfuls of 15 are possible with at least three pieces of each ﬂavor?

assume that you have 50 pennies and three jars, labeled A, B, and -In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar must have at least two pennies put into it?

Find the next four largest 4-combinations of the set {1, 2, 3, 4, 5, 6, 7, 8} after {1, 2, 3, 5}.

If the permutations of 1,2,3,4,5,6 are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation immediately before 534126 .

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical, -How many handfuls of 15 are possible with at least one piece of each ﬂavor?

If the permutations of 1,2,3,4,5,6 are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation in position #483.

assume that you have 50 pennies and three jars, labeled A, B, and -In how many ways can you put the pennies in the jars, assuming that the pennies are identical and each jar must have an even number of pennies put into it?

If the permutations of 1,2,3,4,5,6 are written in lexicographic order, with 123456 in position # 1,123465 in position #2, etc., find the permutation immediately after 246531 .

You have a pile of 20 identical blank cards. On each card you draw a circle, a plus, or a square. How many piles of 20 cards are possible?

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each ﬂavor are identical, -How many handfuls of 15 are possible?

Find the next largest permutation in lexicographic order after 52143.

Find the next largest permutation in lexicographic order after 3254781.