## anonymous one year ago Three disjoint subsets are to be formed from a collection of 30 items. The first is to have 10 elements, the second is to have 9 elements, and the third is to have 11 elements. In how many ways can this be done?

1. anonymous

somehow my answer doesnt match up the answer from the book, strange

2. anonymous

$\left(\begin{matrix}30 \\ 10\end{matrix}\right), \left(\begin{matrix}30 \\ 9\end{matrix}\right),\left(\begin{matrix}30 \\ 11\end{matrix}\right)$

3. anonymous

I got 989779465 but the book answer is 5046360719400

4. amistre64

does order matter?

5. amistre64

i think 30C10, then after 10 are chosen its 20C9, etc

6. amistre64

7. amistre64

$\binom{n}{a}\binom{n-a}{b}\binom{n-a-b}{c}...$

8. anonymous

k thank you for the clarification

9. amistre64

yw

10. anonymous

Three disjoint subsets are to be formed from a collection of 30 items. The first is to have 11 elements, the second is to have 9 elements, and the third is to have 10 elements. In how many ways can this be done? that will give the same answer?