# NCERT Class 11-Math՚S: Chapter – 7 Permutations and Combinations Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 42**:

________.

**Answer**:

**Question 43**:

The number of permutations of *n* different objects, taken at a line, when repetitions are allowed, is ________.

**Answer**:

**Question 44**:

The number of different words that can be formed from the letters of the word

INTERMEDIATE such that two vowels never come together is ________.

[**Hint**: Number of ways of arranging 6 consonants of which two are alike is and number of ways of arranging vowels

**Answer**:

**Question 45**:

Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ________

**Answer**:

**Question 46**:

The number of six-digit numbers, all digits of which are odd is ________.

**Answer**:

**Question 47**:

In a football championship, 153 matches were played . Every two teams played one match with each other. The number of teams, participating in the championship is ________.

**Answer**:

**Question 48**:

The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ________.

**Answer**:

**Question 49**:

A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.

[**Hint**: At least 3 men and 2 women: The number of ways . For 2 particular women to be always there: the number of ways . The total number of committees when two particular women are never together Total together.]

**Answer**:

**Question 50**:

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ________.

State whether the statements in Exercises from 51 to 59 True or False? Also give justification.

**Answer**:

**Question 51**:

There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is

**Answer: False**

**Question 52**:

Three letters can be posted in five letterboxes in ways.

**Answer: False**

**Question 53**:

In the permutations of *n* things, taken together, the number of permutations in which particular things occur together is

**Answer: False**

**Question 54**:

In a steamer there are stalls for animals, and there are horses, cows and calves (not less than each) ready to be shipped. They can be loaded in ways.

**Answer: True**

**Question 55**:

If some or all of *n* objects are taken at a time, the number of combinations is .

**Answer: True**

**Question 56**:

There will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It is being given that the balls of the same colour are identical.

**Answer: True**