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
Top Questions on permutations and combinations
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- Priya is organizing seating arrangements for a panel discussion in Mumbai. She has 6 panelists: 2 men & 4 women. They need to be seated in a row such that no two men sit together. In how many ways can this seating arrangement be made?
- SNAP - 2025
- Quantitative Ability and Data Interpretation
- permutations and combinations
- A committee of 3 is to be formed from 5 men and 4 women. It must contain exactly 2 men and 1 woman. How many ways can it be done?
- SNAP - 2025
- Quantitative Ability and Data Interpretation
- permutations and combinations
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
Questions Asked in JEE Main exam
Nature of compounds TeO₂ and TeH₂ is___________ and ______________respectively.
- JEE Main - 2025
- Inorganic chemistry
- Let \( A = [a_{ij}] \) be a matrix of order 3 \(\times\) 3, with \(a_{ij} = (\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \( A^2 \) is \( \alpha + \beta\sqrt{2} \), where \(\alpha, \beta \in \mathbb{Z}\), then \(\alpha + \beta\) is equal to:
- JEE Main - 2025
- Matrices and Determinants
Consider the following sequence of reactions :
Molar mass of the product formed (A) is ______ g mol\(^{-1}\).- JEE Main - 2025
- Organic Chemistry
The magnitude of heat exchanged by a system for the given cyclic process ABC (as shown in the figure) is (in SI units):
- JEE Main - 2025
- Electric charges and fields
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
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.