How many ways can you choose 2 side dishes out of 9?

Answer 1

Assuming you want 2 different side dishes, they can be chosen in 9 × 8 ways, but as the order doesn't matter every combination has been chosen twice so that there are 9 × 8 ÷ 2 = 36 difference choices.

There is a general formula for choosing r different items from a set of n items:

nCr(n, r) = n!/(r!(n-r)!)

where the exclamation mark means "factorial", which is n × (n-1) × (n-2) × ... × 2 × 1. eg 4! = 4 × 3 × 2 × 1 = 24. 0! is defined to be 1.

For 2 items from 9 this gives:

nCr(9, 2) = 9!/(2!(9-2)!) = 9!/(2!7!) = (9 × 8 × 7 × 6 × ... × 1)/((2 × 1) × (7 × 6 × ... × 1)) = (9 × 8)/2 = 36 (as before).