Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: EXERCISE-1

Ten different letters of alphabet are given. Words with four letters are formed from the these letters, then the number of words which have at least one letter repeated is -

The number of ways of arranging the letters $AAAAA, BBB, CCC, D, EE$ and $F$ in a row if no two ‘$C$’s are together :

Number of numbers greater than a million and divisible by $5$ which can be formed by using only the digits $1, 2, 1, 2, 0, 5$ & $2$ is -

The maximum number of different permutations of $4$ letters of the word "EARTHQUAKE" is -

The number of ways in which we can arrange $n$ ladies & $n$ gentlemen at a round table so that $2$ ladies or $2$ gentlemen may not sit next to one another is -

The number of proper divisors of $a^p{b}^q{c}^r{d}^s$ where $a, b, c, d$ are primes & $p, q, r, s\in N$ is -

The sum of all numbers greater than $1000$ formed by using the digits $1, 3, 5, 7$ such that no digit is being repeated in any number is -

Number of ways in which $25$ identical pens can be distributed among Keshav, Madhav, Mukund and Radhika such that at least $1, 2, 3$ & $4$ pens are given to Keshav, Madhav, Mukund and Radhika respectively, is -