Combinatorics and probability

Question

A typical platoon consists of 20 soldiers. If there are 30 soldiers available to create a platoon. How many different platoons are possible? 

Answer 1

The number of ways to choose r objects from among n when repetitions aren't allowed and order of selection doesnt matter is nCr ("n choose r"). There are 30 choose 20 platoons. 30 choose 20 can be computed as

30!/(20! × (30-20)!) = 30 × 29 × ... × 21 / (10 × 9 × ... × 1)