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- 1. In how many different number of ways 4 boys and 2 girls can sit on a bench?

A.620

B.640

C.720

D.None of these

Answer & Explanation

Answer: Option C

Explanation:^{n}p

_{n}= n!

^{6}p

_{6}= 6 × 5 × 4 × 3 × 2 × 1 = 720

- 2. A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?

A.600

B.300

C.900

D.750

Answer & Explanation

Answer: Option A

Explanation:**Two men, three women and one child can be selected in**

= (4 x 3)/(2 x 1) x (6 x 5 x 4)/(3 x 2) x 5

^{4}C_{2}x^{6}C_{3}x^{5}C_{1}ways= (4 x 3)/(2 x 1) x (6 x 5 x 4)/(3 x 2) x 5

**= 600 ways.**

- 3. Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?

A.32

B.30

C.55

D.29

Answer & Explanation

Answer: Option A

Explanation:**We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.**

Hence, the required number of straight lines

Hence, the required number of straight lines

^{11}C_{2}-^{6}C_{2}-^{5}C_{2}+ 1 + 1 = 55 - 15 - 10 -+ 2 = 32- 4. A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?

A.

^{22}C_{10}B.

^{22}C_{10}+^{20}C_{10}C.

^{22}C_{10}+ 1D.

^{22}C_{10}- 1
Answer & Explanation

Answer: Option D

Explanation:**The total number of ways of forming the group of ten representatives is**

The total number of ways of forming the group that consists of no seniors is

The required number of ways =

^{22}C_{10}.The total number of ways of forming the group that consists of no seniors is

^{10}C_{10}= 1 wayThe required number of ways =

^{22}C_{10}- 1- 5. A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?

A.300

B.600

C.450

D.750

Answer & Explanation

Answer: Option B

Explanation:**The number of ways of selecting three men, two women and three children is:**

=

= (4 x 3 x 2)/(3 x 2 x 1) x (6 x 5)/(2 x 1) x (5 x 4 x 3)/(3 x 2 x 1)

= 4 x 15 x 10

= 600 ways.

=

^{4}C_{3}x^{6}C_{2}x^{5}C_{3}= (4 x 3 x 2)/(3 x 2 x 1) x (6 x 5)/(2 x 1) x (5 x 4 x 3)/(3 x 2 x 1)

= 4 x 15 x 10

= 600 ways.

**To whom this Permutations Questions and Answers section is beneficial?**

Students can learn and improve on their skillset for using Verbal Ability effectively and can also prepare for competitive examinations like...

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