Question 980253
b)	Four names are drawn from among the 24 members of a club for the offices of president, vice-president, treasurer and secretary. In how many different ways can this be done?


Ans: Number of ways in which 4 names can be chosen from 24 members= 24C4

Since they are being chosen for 4 different posts, they can be rearranged among themselves for these 4 posts in 4! ways.

Total number of ways = 24C4 * 4! = 24*23*22*21

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It could also be directly arrived as 24P4 (as order is important here).

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This could also be arrived by visualizing that say, for the post of President number of people available = 24.

Once President is chosen, the post of Vice President can be filled in by rest of 23 people = 23 ways.


Once VP is chosen, the posts of treasurer and secretary can be filled in 22 and 21 ways respectively.


Total ways= 24*23*22*21.

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c)	How many different committees of two chemists and one physicist can be formed from the four chemists and three physicists on the faculty of small college?


Ans: Total ways in which committee can be formed = Number of ways of selecting 2 chemists out of 4 chemists x Number of ways of selecting 1 physicist out of 3 physicists.

= 4c2* 3c1 = 6*3= 18



Thanks,
PRD
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