Question 980253: a) In how many different ways can the five starting players of a basketball team be introduced to the public?
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?
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?
Answer by onlinepsa(22)   (Show Source):
You can put this solution on YOUR website! 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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