JEE Mains · Maths · STD 11 - 6. permutation and combination
The largest \(\mathrm{n} \in \mathrm{N}\) such that \(3^{\mathrm{n}}\) divides 50 ! is:
- A 21
- B 22
- C 20
- D 23
Answer & Solution
Correct Answer
(B) 22
Step-by-step Solution
Detailed explanation
\(2^\alpha \cdot 3^\beta \cdot 5^\gamma\) \(\mathrm{B}=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right]\) \(=16+5+1\) \(=2\) Maximum value of \(n\) is 22
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