Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: KCET (UG) 2020

The number of $4$ digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is

The number of ways in which $5$ girls and $3$ boys can be seated in a row so that no two boys are together is

If $A=\{1,2,3,4,5,6\},$ then the number of subsets of $A$ which contain atleast two elements is

Everybody in a room shakes hands with everybody else. The total number of handshakes is $45$. The total number of persons in the room is

A student has to answer $10$ questions, choosing at least $4$ from each of the parts $A$ and $B.$ If there are $6$ questions in part $A$ and $7$ in part $B,$ then the number of ways can the student choose $10$ questions is