Mathematics Mcqs

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?

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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. 42
D. 60
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 = ⁶C₃ = (6 * 5 * 4)/6 = 20.

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

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

A. 4000
B. 2160
C. 4320
D. 5300
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 ⁶P₆ ways.
The required number of ways = 6(6!) = 4320

In how many ways can live boys and three girls sit in a row such that all boys sit together?

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In how many ways can live boys and three girls sit in a row such that all boys sit together?

A. 4800
B. 5760
C. 2880
D. 15000
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 * 120 = 2880.