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?

Question

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

I got 989779465
but the book answer is 5046360719400

amistre64 · Answer

does order matter?

amistre64 · Answer

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

amistre64 · Answer

attachment

amistre64 · Answer

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

anonymous · Answer

k thank you for the clarification

amistre64 · Answer

yw

anonymous · Answer

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?