A girl is making a cookie recipe. She has forgotten the order of how the first five ingredients should be mixed. There is a total of 9 ingredients in the recipe.

Question

How many ways can the first five ingredients be mixed?

Options: I got 15120

1. 120
2. 504
3. 3024
4. 15120

Answer 1

Hey!

I want to back you up on this one. For lists where order does/doesn't matter, we simply use the factorial function! BUT since this order DOES matter, this decreases with every succeeding factor!

First, we know we have 9 ingredients. IF we were to use every single one, it would be 9!. However, since we only need the first five, we have five slots (once an ingredient is used, I'm assuming it can't be replaced)....

_ x _ x _ x _ x _ = ?

9 x 8 x 7 x 6 x 5.

= 15,120

(P.S. in scenarios where it is explicitly stated that items aren't replaced, each factor decreases. If the ingredients were replaced/used twice, we would've had 9 x 9 x 9 x 9 x 9);.