# NCERT Class 11-Math's: Chapter –7 Permutations and Combinations Part 5

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**7.3 EXERCISE**

**Short Answer Type**

**Question 1:**

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

[**Hint:** 2 women occupy the chair, from 1 to 4 in ways and men occupy the remaining chairs in ways.]

**Answer:**

**Question 2:**

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?

[**Hint:** In each case number of words beginning with A, C, H, I is ]

**Answer:**

**Question 3:**

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

**Answer:**

**Question 4:**

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

[**Hint:** Number of straight lines =]

**Answer:**

**Question 5:**

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

**Answer:**

**Question 6:**

How many committee of five persons with a chairperson can be selected from 12 persons.

[**Hint:** Chairman can be selected in 12 ways and remaining in.]

**Answer:**

**Question 7:**

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

**Answer:**

**Question 8:**

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.

**Answer:**

**Question 9:**

Find the number of permutations of distinct things taken *r* together, in which 3 particular things must occur together.

**Answer:**

**Question 10:**

Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together

**Answer:**

**Question 11:**

Find the number of positive integers greater than and less than which are divisible by 5, provided that no digit is to be repeated.

**Answer:**

**Question 12:**

There are persons named . Out of persons, 5 persons are to be arranged in a line such that in each arrangement must occur whereas and do not occur. Find the number of such possible arrangements.

[**Hint:** Required number of arrangement ]

**Answer:**

Formula:-

Given:- There are person named .

Number of ways of arrangement

Number of ways arrangement of other

Therefore, required number of arrangement