In how many ways can I choose 2 cooks on a backpacking trip with 8 people if any of the 8 people may be cooks?

 

We can use the combination formula: C(n, k) = n! / (k! * (n-k)!), where n is the total number of people (8) and k is the number to choose (2). So, we need C(8, 2) = 8! / (2! * 6!).

Calculate the factorials:

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

2! = 2 * 1 = 2

Plugging in: C(8, 2) = (8 * 7 * 6!) / (2 * 1 * 6!). The 6! cancels out, leaving (8 * 7) / (2 * 1) = 56 / 2 = 28.

Alternatively, the formula simplifies to C(n, k) = [n * (n-1) * ... * (n-k+1)] / k!. For n=8, k=2: C(8, 2) = (8 * 7) / (2 * 1) = 56 / 2 = 28.

 

mercurym999