# Combinatorics Question Help; # of ways to choose 4 distinct officials from a city?

there are $n \ge 4$ people in a city. And the city has its officials, consisting of 1 mayor and 3 vice-mayors. The entire board consists of 4 distinct students. Prove that by counting. In 2 different methods, count the number of ways to choose a board of officials

$$n \binom{n-1}{3} = (n-3)\binom{n}{3}$$

Any tips on two ways to help me started? I am stuck on this question and just need some starting help!

• Can you go to the definition $\binom{n}{k}$ = $\frac{n!}{k!(n-k)!}$? – graydad Sep 28 '14 at 17:22
• Rolled back destructive edit. – apnorton Oct 1 '14 at 0:03