# NCERT Class 11 Mathematics Solutions: Chapter 7 –Permutation and Combinations Miscellaneous Exercise Part 3

1. In an examination, a question paper consists of questions divided into two parts i.e., Part I and Part II, containing questions, respectively. A student is required to attempt questions in all, selecting at least from each part. In how many ways can a student select the questions?

It is given that the question paper consists of questions divided into two parts – Part I and Part II, containing questions, respectively.

A student has to attempt questions, selecting at least from each part. This can be done as follows.

(a) 3 questions from part questions from part II

(b) 4 questions from part questions from part II

(c) 5 questions from part questions from part II

questions from part I and questions from part II can be selected in ways.

questions from part I and questions from part II can be selected in ways.

questions from part I and questions from part II can be selected in ways.

So, required number of ways of selecting questions

2. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

From a deck of cards, -card combinations have to be made in such a way that in each selection of cards, there is exactly one king.

In a deck of cards, there are kings.

1 king can be selected out of 4 kings in ways.

cards out of the remaining cards can be selected in ways.

Thus, the required number of -card combinations is

3. It is required to seat men and women in a row so that the women occupy the even places. How many such arrangements are possible?