Basic counting Problem - confirmation of solution

At a certain meeting of 25 people, they decide to select a committee, which would have a chairman and 2 members. How many ways are there to do it?

There are 25 ways to choose the chairman followed by $24C2$ to choose the two remaining members. So the answer would be $25 * 24C2$ = 6900.

I just wanna double check this is the right way to do it. Thanks!

• Yes, that's the right way. The explanation is clear, but I would prefer "For each way of choosing the Chair, there are $\binom{24}{2}$ ways $\dots$." – André Nicolas Oct 16 '15 at 0:00
• Okay thanks for the clarification – person112358 Oct 16 '15 at 0:02
• Can also think of as ${25 \choose 3} \cdot 3$, also equal to 6900, e.g. first choose the 3 members without a chair; for each of these triples there are 3 chaired committees. – Circulwyrd Oct 16 '15 at 0:14