next up previous index
Next: Conditional Probability Up: Enumeration Rules Previous: The matching Problem 10/9

Multinomial Coefficients and applications 10/12

How many ways are there of assigning 10 police officers to 3 different tasks: We saw how the answer comes out to be:

\begin{displaymath}\binom{10}{5} \times \binom{5}{2} \times \binom{3}{3} =\frac{10!}{ 5!
3! 2!}\end{displaymath}

In general there will $ \frac{n!}{k_1!k_2! ...k_r!}$ ways divide up n objects into r different categories so that there will be k1 objects in category 1, k2 in category 2, and so on ( $k_1+k_2+\cdots +k_r=n$).

Susan Holmes
1998-12-07