Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 2: Level 2

How many line segments have both their endpoints located at the vertices of a given cube?

Three and four digit numbers are formed from the digits $1, 3, 5, 6, 8.$ If $e_1$ is number of three digit even numbers with no digit repeated and $e_2$ is number of four digit even numbers with no digit repeated. Also $O_1$ represent the number of three digit odd numbers in which no digit is repeated and $O_2$ represent the number of four digit odd numbers in which no digit is repeated. Then

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 -

Let $P_m$ stand for ${}^{m}P_{m\text{'}}$ then, $1+P_1+2P_2+3P_3+.......+n{P}_n$ is equal to

$n$ different toys have to be distributed among $n$ children. Total number of ways in which these toys can be distributed, so that exactly one child gets no toy, is equal to

There are $n-1$ red balls, $n$ green balls and $n+1$ blue balls in a bag. The number of ways of choosing two balls from the bag that have different colours is $299.$ What is the value of $n$?

A team of four students is to be selected from a total of $12$ students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to

Let $A=\{0, 1, 2, 3, 4, 5, 6, 7\}.$ Then the number of bijective functions $f:A\to A$ such that $f\left(1\right)+f\left(2\right)=3-f\left(3\right)$ is equal to