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# The county-mandated guidelines at a certain community college specify

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Math Expert
Joined: 02 Sep 2009
Posts: 50036
The county-mandated guidelines at a certain community college specify  [#permalink]

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24 Feb 2015, 07:48
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:06) correct 12% (02:21) wrong based on 80 sessions

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The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?

A. 15
B. 30
C. 90
D. 150
E. 360

Kudos for a correct solution.

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Re: The county-mandated guidelines at a certain community college specify  [#permalink]

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24 Feb 2015, 08:23
1
Here we go:

We have to pick one of three specified novels and two from a list of 5 specified plays.

This can be done in

3c1 * 5c2 ways.

3 * 10 = 30

Option B is correct
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The county-mandated guidelines at a certain community college specify  [#permalink]

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24 Feb 2015, 08:52
Bunuel wrote:
The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?

A. 15
B. 30
C. 90
D. 150
E. 360

Kudos for a correct solution.

not a very corrected worded question ....
it contains 'may ' and then talks of 'guarranteed'....
but what the question could be implying, accordingly the answer..
one of three specified novels= 3c1.. two of five plays=5c2..
total=3c1*5c2=3*10=30
ans B..30
however, as we are talking of different readings list, the order may be important ...
these 3 can be then arranged in 3! ways .. ans then becomes 30*6=180..
however with this answer not one of the choices, i think the question means it is selection and not arrangement
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Re: The county-mandated guidelines at a certain community college specify  [#permalink]

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28 Feb 2015, 08:44
Bunuel wrote:
The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?

A. 15
B. 30
C. 90
D. 150
E. 360

Kudos for a correct solution.

No. of ways in which 1 novel can be selected out of 3 = 3C1 = 3 ways
No. of ways in which 2 plays can be selected out of 5 = 5C2 = 10 ways

Hence total number of ways = 3 * 10 = 30
Hence option B

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Posts: 50036
Re: The county-mandated guidelines at a certain community college specify  [#permalink]

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02 Mar 2015, 06:40
Bunuel wrote:
The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?

A. 15
B. 30
C. 90
D. 150
E. 360

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

There are three possibilities for the novel. With the plays, we are taken a combination of 2 from a set of 5 --> n = 5, r = 2, n – r = 3

# of combinations = $$\frac{5!}{2!3!} = \frac{(5)(4)(3)(2)(1)}{(2)(1)(3)(2)(1)} = \frac{(5)(4)}{2} = 10$$

If the plays are P, Q, R, S, and T, then the 10 sets of two are PQ, PR, PS, PT, QR, QS, QT, RS, RT, & ST.
Any of the three novels can be grouped with any of the 10 possible pairs of plays, for a total of 30 possible reading lists.

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Re: The county-mandated guidelines at a certain community college specify  [#permalink]

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29 Jun 2017, 15:10
The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?

$$= 3C1 * 5C2$$

$$= 3 * 10$$

$$= 30$$

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Re: The county-mandated guidelines at a certain community college specify &nbs [#permalink] 29 Jun 2017, 15:10
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