# NCERT Class 11-Math՚s: Chapter – 7 Permutations and Combinations Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 32**:

Every-body in a room shakes hands with everybody else. The total number of hand-shakes is 66. The total number of persons in the room is

(A) 11

(B) 12

(C) 13

(D) 14

**Answer: (B)**

**Question 33**:

The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is

(A)

(B)

(C)

(D)

**Answer: (D)**

**Question 34**:

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

(A) 6

(B) 18

(C) 12

(D) 9

**Answer: (B)**

**Question 35**:

The number of ways in which a team of eleven players can be selected from players always including 2 of them and excluding 4 of them is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 36**:

The number of 5-digit telephone numbers having atleast one of their digits repeated is

(A)

(B)

(C)

(D)

**Answer: (D)**

**Question 37**:

The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is

(A)

(B)

(C)

(D) None

**Answer: (A)**

**Question 38**:

The total number of 9 digit numbers which have all different digits is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 39**:

The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is

(A)

(B)

(C)

(D)

**Answer: (B)**

**Question 40**:

Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is

(A)

(B)

(C)

(D)

[**Hint**: Possible numbers of choosing or not choosing 5 green dyes, 4 blue dyes and 3 red dyes are and , respectively.]

**Answer: (B)**

Fill in the Blanks in the Exercises 41 to 50.

**Question 41**:

If , then ________.

**Answer**: