Question:

Maximum value n such that (66)! is divisible by 3n

Updated On: Aug 19, 2023
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Solution and Explanation

The correct answer is : 31

\(\because\) 3 sis prime number,

\([\frac{66}{3}]+[\frac{66}{3^2}]+[\frac{66}{3^3}]+[\frac{66}{3^4}]+........\)

\(\Rightarrow\) 22+7+2+0+………

= 31

\((66)!=(3)^{31}........\)

maximum value of n=31

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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.