Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

What is the number of ways in which the letters of the word $\mathrm{ABLE}$ can be arranged so that the vowels occupy even places?

What is the maximum number of points of intersection of $5$ non-overlapping circles?

What is the number of diagonals of an octagon?

If $P\left(n, r\right)=2520$ and $C\left(n, r\right)=21,$ then what is the value of $C\left(n+1, r+1\right) ?$

If $n!$ has $17$ zeros, then what is the value of $n?$

There are $10$ points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?

From $6$ programmers and $4$ typists, an office wants to recruit $5$ people. What is the number of ways this can be done so as to recruit atleast one typist?

How many three digit even numbers can be formed using the digits $1, 2, 3, 4$ and $5$ when repetition of digits is not allowed?