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

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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?

Answer:

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.

Answer:

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?

Answer:

men and women are to be seated in a row such that the women occupy the even places.

The men can be seated in ways.

For each arrangement, the women can be seated only at the cross marked places (so that women occupy the even places).

So, the women can be seated in ways.

Thus, possible number of arrangements