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# The purchaser of a certain car must choose 2 of 5 special options and

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Math Expert
Joined: 02 Sep 2009
Posts: 65112
The purchaser of a certain car must choose 2 of 5 special options and  [#permalink]

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27 Feb 2019, 22:19
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Question Stats:

85% (00:59) correct 15% (01:33) wrong based on 87 sessions

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The purchaser of a certain car must choose 2 of 5 special options and 5 of 6 interior features. How many different combinations of options and features are available to the purchaser?

A. 10
B. 16
C. 18
D. 30
E. 60

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Re: The purchaser of a certain car must choose 2 of 5 special options and  [#permalink]

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28 Feb 2019, 03:02
Bunuel wrote:
The purchaser of a certain car must choose 2 of 5 special options and 5 of 6 interior features. How many different combinations of options and features are available to the purchaser?

A. 10
B. 16
C. 18
D. 30
E. 60

options avail 5c2* 6c5
10*6
60
IMO E
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Posts: 804
Location: India
Re: The purchaser of a certain car must choose 2 of 5 special options and  [#permalink]

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29 Mar 2020, 07:51
Bunuel wrote:
The purchaser of a certain car must choose 2 of 5 special options and 5 of 6 interior features. How many different combinations of options and features are available to the purchaser?

A. 10
B. 16
C. 18
D. 30
E. 60

Solution

• The number of ways in which the car can be chosen = $$5C2 = \frac{5!}{2!*3!} = 10$$
• The number of ways in which the interior can be selected = $$6C5 = 6$$
o The total number of combinations of option and feature = $$10*6= 60$$
Hence, the correct answer is Option E.
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Re: The purchaser of a certain car must choose 2 of 5 special options and  [#permalink]

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08 Apr 2020, 16:52
Bunuel wrote:
The purchaser of a certain car must choose 2 of 5 special options and 5 of 6 interior features. How many different combinations of options and features are available to the purchaser?

A. 10
B. 16
C. 18
D. 30
E. 60

5C2 * 6C5
5C2= 5!/(3!2!) = 10
6C5 = 6

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Re: The purchaser of a certain car must choose 2 of 5 special options and  [#permalink]

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11 Apr 2020, 04:55
Bunuel wrote:
The purchaser of a certain car must choose 2 of 5 special options and 5 of 6 interior features. How many different combinations of options and features are available to the purchaser?

A. 10
B. 16
C. 18
D. 30
E. 60

The number of possible combinations is:

5C2 * 6C5

(5 x 4)/2! * 6 = 5 x 4 x 3 = 60

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Re: The purchaser of a certain car must choose 2 of 5 special options and   [#permalink] 11 Apr 2020, 04:55