JEE Mains · Maths · STD 11 - 6. permutation and combination
A group of students comprises of \(5\) boys and \(n\) girls. If the number of ways, in which a team of \(3\) students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is \(1750\), then \(n\) is equal to
- A \(24\)
- B \(28\)
- C \(27\)
- D \(25\)
Answer & Solution
Correct Answer
(D) \(25\)
Step-by-step Solution
Detailed explanation
Given \(5\) boys and \(n\) girls Total ways of farming team of \(3\) Members under given condition \({ = ^5}{C_1}{.^n}{C_2}{ + ^5}{C_2}{.^n}{C_1}\) \({ \Rightarrow ^5}{C_1}{.^n}{C_2}{ + ^5}{C_2}{.^n}{C_1} = 1750\) \( \Rightarrow \frac{{5n(n - 1)}}{2} + 10n = 1750\)…
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