QJEEAdv24Ma8054: JEE Advanced 2024 Mathematics - Class 11 JEEAdv24Ma8054 Solution: A group of 9 students, , is to be divided to form three teams , …

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QJEEAdv24Ma8054: JEE Advanced 2024 Mathematics - Class 11 JEEAdv24Ma8054 Solution: A group of 9 students, , is to be divided to form three teams , …

A group of 9 students, $s_1, s_2, \ldots, s_9$ , is to be divided to form three teams $X, Y$ , and $Z$ of sizes 2,3 , and 4 , respectively. Suppose that $s_1$ cannot be selected for the team $X$ , and $s_2$ cannot be selected for the team $Y$ . Then the number of ways to form such teams, is ____________.

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Accepted Answer

$\begin{matrix} x & y & z \\ 2 & 3 & 4 \\ {\overset{―}{S}}_{1} & {\overset{―}{S}}_{2} \end{matrix}$

C-i) When x does not contain S $_{1}$ , but contains S $_{2}$

$\underset{f o r x}{^{7} C_{1}} \times \underset{f o r y, z}{\frac{7!}{3! 4!}} = 245$

C-ii) When x does not contain $S_{1}, S_{2}$ and y does not contain $S_{2}$

i.e. $\underset{f o r x}{^{7} C_{2}} \times \underset{f o r y, z}{\frac{6!}{3! 3!}} = 420$

so total No. of ways 665

QJEEAdv24Ma8054: JEE Advanced 2024 Mathematics - Class 11 JEEAdv24Ma8054 Solution: A group of 9 students, , is to be divided to form three teams , …

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