JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of onto functions \(f\) from \(\{1, 2, 3, …, 20\}\) only \(\{1, 2, 3, …, 20\}\) such that \(f(k)\) is a multiple of \(3\), whenever \(k\) is a multiple of \(4\), is
- A \({6^5} \times \left( {15} \right)!\)
- B \(5! \times 6!\)
- C \(\left( {15} \right)! \times 6!\)
- D \({5^6} \times 15\)
Answer & Solution
Correct Answer
(C) \(\left( {15} \right)! \times 6!\)
Step-by-step Solution
Detailed explanation
\(k = \{ 4,8,12,16,20\} \) \(f(k)\,\) can takes the values \(\{ 3,6,9,12,15,18\} \) Number of ways \({ = ^6}{C_5}.5!\) \(\therefore \) Total number of onto functions \({ = ^6}{C_5}.5!(15!)\) \( = (6!)(15!)\)
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