Hello, cnmath16!

a) How many 4-digit numbers can be formed from the set

if there is no repetiton?

The first digit cannot be 0: 6 choices.

Second digit: 6 choices.

Third digit: 5 choices.

Fourth digit: 4 choices.

There are: . possible four-digit numbers.

How many numbers doc) How many of the numbers in part a) contain a 3?notcontain a 3?

. . The first digit cannot be 0 or 3: 5 choices.

. . Second digit: 5 choices.

. . Third digit: 4 choices.

. . Fourth digit: 3 choices

There are: . numbers without a 3.

Therefore, there are: . numbers with a 3.

There are two cases to consider:d) How many of the numbers in part a) are divisible by 5?

. . (1) The number ends in 5.

. . (2) The number ends in 0.

(1) The number ends in 5: . _ _ _ 5

. . The first digit must not be 0 or 5: 5 choices.

. . Second digit: 5 choices.

. . Third digit: 4 choices.

There are: . numbers ending in 5.

(2) The number ends in 0: ._ _ _ 0

. . First digit: 6 choices.

. . Second digit: 5 choices.

. . Third digit: 4 choices.

There are: . numbers ending in 0.

Therefore, there are: . numbers divisible by 5.