JEE Mains · Maths · STD 11 - 6. permutation and combination
The students \(S _{1}, S _{2}, \ldots \ldots, S _{10}\) 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 ........ .
- A \(63300\)
- B \(42580\)
- C \(15325\)
- D \(31650\)
Answer & Solution
Correct Answer
(D) \(31650\)
Step-by-step Solution
Detailed explanation
If group \(C\) has one student then number of groups \({ }^{10} C _{1}\left[2^{9}-2\right]=5100\) If group \(C\) has two students then number of groups \({ }^{10} C _{2}\left[2^{8}-2\right]=11430\) If group \(C\) has three students then number of groups…
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