1. Out of the blouse in her closet. Precious wants to choose five blouses to bring for an out of town trip. How many ways can she choose the blouses?

Question

1. Out of the blouse in her closet. Precious wants to choose five blouses to bring for an out of town trip. How many ways can she choose the blouses?

Answer 1

If she has n blouses, there's nC5 different ways

nC5 = n!/(n-5)!5!

for example, if she has 20 blouses then there are 20!/15!5!

= 20x19x18x17x16/5x4x3x2 = 19x3x17x16 = 15504 different ways

If the order somehow matters then you'd calculate permutations instead of combinations. Some calculators have functions for both

the key usually says "nCr" or "nPr" for each.

in your example r = 5

if order mattered and you wanted permutations, then 20P5 = 1,860,480 ways, click on 20, then on nPr, then on 5, out comes the answer as the calculator does the work for you.

Answer 2

The order in which she chooses the blouses doesn't matter, so this is a combination, not a permutation.

If she has n unique blouses in her closet, she can choose 5 blouses in _nC₅ ways.