Sarvesh K Verma Solutions for Chapter: Permutations & Combinations, Exercise 11: CAT - Test Questions Helping You Bell the CAT

Spiritual Guru H. E. Dalai Lama is on a world tour to speak on peace and compassion. His itinerary mentions only four continents - Asia, Africa, Europe and America - for this visit. What is the minimum number of countries he should visit to ensure that at least $21$ Asian or at least $16$ African or at least $11$ European or at least$6$American countries must be visited?

Arya, Bran, Cersei, Daenerys, Petyr, and Tyrion are seated in six chairs placed in a row. Maximum how many seating arrangements are possible if A must sit next to B, but P cannot sit next to T?

How many $6$ digit telephone numbers can be formed if each number starts with $91$ and sum of the digits is equal to $16 ?$

Jwala Gutta and P. V. Sindhu play a one-day serie They stop playing matches as soon as one of them wave $3$ matches and in this series no match is drawn. In how many ways can this series be won?

Let there be a random number $\mathrm{n}$ such that the product of its digits is $6 .$ How many values of $\mathrm{n}$ are there, if $\mathrm{n}$ lies between ${10}^9$ and ${10}^{10}?$

Sarvesh wants to prepare a bouquet with roses, lilies, orchids and carnations, so he walked into a large garden of flowers. In how many ways can he prepare a bouquet of $15$ flowers such that he selects at least $1$ rose, $2$ lilies, $3$ orchids and $4$ carnations for his bouquet?

The number of non-negative integral solutions of $x_1+x_2+x_3+x_4\le n$ (where $n$ is a positive integer) is