JEE PYQ: Permutation And Combination Question 8
Question 8 - 2021 (24 Feb Shift 2)
The students $S_1, S_2, \ldots, S_{10}$ are to be divided into 3 groups $A$, $B$ and $C$ such that each group has at least one student and the group $C$ has at most 3 students. Then the total number of possibilities of forming such groups is
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Answer: 31650
Solution
$= {}^{10}C_1[2^9 - 2] + {}^{10}C_2[2^8 - 2] + {}^{10}C_3[2^7 - 2] = 2^7[{}^{10}C_1 \times 4 + {}^{10}C_2 \times 2 + {}^{10}C_3] - 20 - 90 - 240 = 128(40 + 90 + 120) - 350 = 128 \times 250 - 350 = 31650$.
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