MATH SOLVE

4 months ago

Q:
# a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs

Accepted Solution

A:

Well this is a permutation/combination problem. If the order that the four songs is in does not matter then it will be a combination, if the order does matter it will be a permutation.

The formula for combinations is: n!/r!(n-r)! where n is the total number possible options and r is the number taken at a time. For this problem n = 12 and r = 5

12!/5!7! = 792 different possible combinations.

The formula for a permutation is n!/(n-r)! where n and r represent the same things as above.

12!/7! = 95,040 different possible permutations

The reason for more permutation than combinations is because if you have 12 songs think of them as 1,2,3,4,5,6,7,8,9,10,11,12. Under a combination songs 1,3,6,9 and 3,6,1,9 are the same, but in a permutation the order matters so these are both different possible outcomes.

The formula for combinations is: n!/r!(n-r)! where n is the total number possible options and r is the number taken at a time. For this problem n = 12 and r = 5

12!/5!7! = 792 different possible combinations.

The formula for a permutation is n!/(n-r)! where n and r represent the same things as above.

12!/7! = 95,040 different possible permutations

The reason for more permutation than combinations is because if you have 12 songs think of them as 1,2,3,4,5,6,7,8,9,10,11,12. Under a combination songs 1,3,6,9 and 3,6,1,9 are the same, but in a permutation the order matters so these are both different possible outcomes.