The U.S. Senate has 100 members. Suppose that it is desired to place each senator on exactly 1 of 7 possible committees. The first committee has 22 members, the second has 13, the third has 10, the fourth has 5, the fifth has 16, and the sixth and seventh have 17 apiece. In how many ways can these committees be formed?

Question

anonymous · Answer

Ohh I was typing a long equation and I lost it.

anonymous · Answer

I got this:

anonymous · Answer

$$C(100,22)\cdot C(78,13)\cdot C(65,10)\cdot C(55,5)\cdot$$

anonymous · Answer

$$C(50,16)\cdot C(34,17)\cdot C(17,17)$$

anonymous · Answer

$$=1.156\times10^{76}$$

anonymous · Answer

I think Its wrong because it is a very big number.

anonymous · Answer

What do you think?

across · Answer

If with $C(x,y)$ you mean $x$ choose $y$, then your thought process seems correct.

across · Answer

Or, more formally,$$C(x,y)=\frac{x!}{y!(x-y)!}.$$

anonymous · Answer

So that means my result is correct. I'm very surprised then. Thank you across.