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A company has 3 directors and 5 managers. How many different

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A company has 3 directors and 5 managers. How many different  [#permalink]

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New post Updated on: 16 Apr 2014, 23:55
1
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00:00
A
B
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D
E

Difficulty:

  35% (medium)

Question Stats:

67% (02:03) correct 33% (02:44) wrong based on 73 sessions

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A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?

A. 500
B. 720
C. 4500
D. 25
E. 55

Originally posted by tauchmeister on 16 Apr 2014, 14:53.
Last edited by Bunuel on 16 Apr 2014, 23:55, edited 1 time in total.
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Re: A company has 3 directors and 5 managers  [#permalink]

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New post 16 Apr 2014, 18:33
3
atleast one means exactly one and more than one.

different committees with 5 people can be chosen having at least 1 director is
(3c1*5c4) + (3c2*5c3) + (3c3*5c2) = 55;
Hence E.
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Re: A company has 3 directors and 5 managers. How many different  [#permalink]

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New post 16 Apr 2014, 23:59
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Re: A company has 3 directors and 5 managers. How many different  [#permalink]

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New post 21 Jun 2019, 10:35
tauchmeister wrote:
A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?

A. 500
B. 720
C. 4500
D. 25
E. 55


We can use the equation:

Number of committees with at least director = total number of committees - number of committees with no directors.

The total number of committees can be formed in 8C5 ways:

8C5 = 8!/(5! x 3!) = (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2) = 8 x 7 = 56
The number of committees that can be formed with no directors is 5C5 = 1.

Thus, the number of committees with at least one director is 56 - 1 = 55.

Answer: E
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Re: A company has 3 directors and 5 managers. How many different   [#permalink] 21 Jun 2019, 10:35

A company has 3 directors and 5 managers. How many different

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