Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: CUSAT CAT 2017

The largest non-negative integer $k$ such that ${24}^k$ divides $13!$ is

How many odd numbers of six significant digits can be formed with the digits $0, 1, 2, 5, 6, 7$ when no digit is repeated?

The number of distinct primes dividing $12!+13!+14!$ Is

If $m={}^{n}C_2$, then ${}^{m}C_2$ is equal to -

The number of sides of a polygon with $44$ diagonals is

$n$-similar balls each of weight $w$ when weighed in pairs the sum of the weights of all possible pairs is $120$ when they are weighed in triplets the sum of the weights comes out to be $480$ for all possible triplets, then $n$ is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is