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