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

If $\sum _{k=1}^{n-r} {}^{n-k}C_r={}^{x}C_y$ then

Set of values of $r$ for which, ${}^{18}C_{r-2}+2·{}^{18}C_{r-1}+{}^{18}C_r\ge {}^{20}C_{13}$ contains

A road network as shown in the figure connect four cities. In how many ways can you start from any city (say A) and come back to it without travelling on the same road more than once ?

The number of ways of choosing a committee of $2$ women & $3$ men from $5$ women & $6$ men, if Mr. $A$ refuses to serve on the committee if Mr. $B$ is a member & Mr. $B$ can only serve, if Miss $C$ is the member of the committee, is -

Sameer has to make a telephone call to his friend Harish, Unfortunately he does not remember the $7$ digit phone number. But he remembers that the first three digits are $635$ or $674$, the number is odd and there is exactly one $9$ in the number. The maximum number of trials that Sameer has to make to be successful is -

The number of solutions of $x_1+x_2+x_3=51$ ($x_1, x_2, x_3$ being odd natural numbers) is : -

The number of positive integral solutions of the equation $x_1{x}_2{x}_3=60$ is :-

Total number of even divisors of $2079000$ which are divisible by $15$ are -