how many different ways

[javaiscrazy]

4 cleaners, 5 cooks and 3 bosses are needed for the company.
13 cleaners, 16 cooks and 9 bosses apply for the company.
How many different ways can be used to establish this company?

- I think that the answer is 13 * 16 * 9 = correct?

 

[pka]

4 cleaners, 5 cooks and 3 bosses are needed for the company.
13 cleaners, 16 cooks and 9 bosses apply for the company.
How many different ways can be used to establish this company?

Using the notation \(\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\)
the answer is \(\displaystyle \binom{13}{4}\cdot \binom{16}{5}\cdot \binom{9}{3}\).