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- 6. 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 5 seniors and 5 juniors?

A.

^{12}C_{7}=^{10}C_{7}B.

^{10}C_{5}=^{12}C_{7}C.

^{12}C_{5}=^{12}C_{5}D.

^{12}C_{5}=^{12}C_{7}
Answer & Explanation

Answer: Option D

Explanation:**Here, five seniors out of 12 seniors can be selected in**

=

=

^{12}C_{5}ways. Also, five juniors out of ten juniors can be selected^{10}C_{5}ways. Hence the total number of different ways of selection=

^{12}C_{5}x^{10}C_{5}=^{12}C_{7}x^{10}C_{5}=

^{12}C_{5}=^{12}C_{7}- 7. In how many ways can live boys and three girls sit in a row such that all boys sit together?

A.3800

B.4760

C.2880

D.1401

Answer & Explanation

Answer: Option C

Explanation:**Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.**

Required number of arrangements = 4! * 5! = 24 x 120 = 2880.

Required number of arrangements = 4! * 5! = 24 x 120 = 2880.

- 8. The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is

A.2010

B.2120

C.4320

D.4322

Answer & Explanation

Answer: Option C

Explanation:**x Not younger_______ ↑**

The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in

The required number of ways = 6(6!) = 4320

The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in

^{6}C_{6}ways.The required number of ways = 6(6!) = 4320

- 9. A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?

A.20

B.54

C.40

D.32

Answer & Explanation

Answer: Option A

Explanation:**There are three ladies and five gentlemen and a committee of 5 members to be formed.**

Number of ways such that two ladies are always included in the committee =

Number of ways such that two ladies are always included in the committee =

^{6}C_{3}= (6 x 5 x 4)/6 = 20.- 10. The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -

A.24

B.23

C.119

D.120

Answer & Explanation

Answer: Option C

Explanation:**Number of words which can be formed = 5! - 1 = 120 - 1 = 119.**

**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...

- All I.B.P.S and Public Sector Bank Competitive Exam
- Common Aptitude Test (CAT) Exams
- UPSC Paper-II or CSAT Exams
- SSC Competitive Exams
- Defence Competitive Exams
- L.I.C / G.I.C AO and Clerk Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- Career Aptitude Test (IT Companies) and etc.