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

A subset $B$ of the set of first $100$ positive integers has the property that no two elements of $B$ sum to $125 .$ What is the maximum possible number of elements in B?

Kumar never lies except on Tuesdays. On Tuesdays, he always lies. On how many days of the week can he say "If I did not lie yesterday then I will lie tomorrow" ?

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

There are several tea cups in the kitchen, some with handles and the others without handles. The number of ways of selecting two cups without a handle and three with a handle is exactly $1200.$ What is the maximum possible number of cups in the kitchen?

A parallelogram is cut by two sets of $n$ parallel lines, parallel to the sides of the parallelogram. The number of parallelograms so formed is

There are five cities $A, B, C, D, E$ on a certain island. Each city is connected to every other city by road. In how many ways can a person starting from city $A$ come back to $A$ after visiting some cities without visiting a city more than once and without taking the same road more than once? (The order in which he visits the cities also matters: e.g., the routes $A\to B\to C\to A$ and $A\to C\to B\to A$ are different)

There are $17$ cricket players, out of which $5$ players can bowl. In how many ways can a team of $11$ players be selected so as to include $3$ bowlers?