# NCERT Class 11-Math՚S: Chapter – 7 Permutations and Combinations Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 13**:

There are lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.

[**Hint**: Required number ] .

**Answer**:

Formula:-

(ii)

Given:- number of lamps in a hall

One of them can be switched on independently

Find the number of ways in which the hall can be illuminated

**Question 14**:

A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw.

[**Hint**: Required number of ways

**Answer**:

Formula:-

Number of ways drawing at least one black ball

**Question 15**:

If and , then find

[**Hint**: Form equation using to find the value of .]

**Answer**:

**Question 16**:

Find the number of integers greater than that can be formed with the digits and 9 where no digits are repeated.

[**Hint**: Besides 4 digit integers greater than , five digit integers are always greater than .]

**Answer**:

**Question 17**:

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?

**Answer**:

**Question 18**:

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?

**Answer**:

**Question 19**:

In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.

**Answer**:

**Question 20**:

A convex polygon has diagonals. Find the number of its sides.

[**Hint**: Polygon of *n* sides has number of diagonals.]

**Answer**:

## Long Answer Type Questions

**Question 21**:

18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

**Answer**:

**Question 22**:

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if (a) they can be of any colour (b) two must be white and two red and (c) they must all be of the same colour.

**Answer**:

(a)

(b)

(C)