The largest n ∈ N such that 3 n divides 50 ! is:

2 α ⋅ 3 β ⋅ 5 γ B = [ 3 50 ] + [ 3 2 50 ] + [ 3 3 50 ] + [ 3 4 50 ] = 16 + 5 + 1 = 2 Maximum value of n is 22

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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minPYQ_2025

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The largest $n \in N$ such that $3^{n}$ divides 50 ! is:

Options:

Answer:

Solution:

$2^{α} \cdot 3^{β} \cdot 5^{γ}$
$B = [\frac{50}{3}] + [\frac{50}{3 ^{2}}] + [\frac{50}{3 ^{3}}] + [\frac{50}{3 ^{4}}]$
$= 16 + 5 + 1$
$= 2$
Maximum value of $n$ is 22

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: PYQ_2025

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