SOLUTION: If you have 20 students in your class how many different ways can a committee of 5 be chosen if 1 person on the committee will be the president?

Question 398228: If you have 20 students in your class how many different ways can a committee of 5 be chosen if 1 person on the committee will be the president?
Found 2 solutions by stanbon, sudhanshu_kmr:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If you have 20 students in your class how many different ways can a committee of 5 be chosen if 1 person on the committee will be the president?
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I guess the president has been determined before you form the
committee of 5. So you really only have 4 choices from a set
of 19 people.
But that answer is 19C4 = 3876.
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Something is rotten in Denmark. (that's an old phrase
for expressing the fact that the problem is confusing)
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Cheers,
Stan H.

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Cheers,
Stan H.
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

it can be solved by two ways......

1) no. of ways to choose a president for committee = 20

no. of ways to choose 4 another members from remaining 19 = 19C4
total no. of ways = 20 * 19C4
= 77520

2) no. of ways to choose committee i.e 5 members from 20 = 20C5
no. of ways to select a president in a committee = 5
total no. of ways = 20C5 * 5

= 77520

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