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In how many ways can 2 prizes (in Science and Maths) be awarded to 15

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Bunuel
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In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   03 Jan 2021, 15:35
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In how many ways can 2 prizes (in Science and Maths) be awarded to 15 students?

A. 190
B. 195
C. 205
D. 210
E. 225
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E
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globaldesi
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   03 Jan 2021, 22:10
first award science can go to 15 peole,
Second award can go to 15 people
so total ways
15*15 = 225
E IMO
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TarunKumar1234
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   03 Jan 2021, 23:36
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Case1: Both awards are given to 1 student (She or He the best student. :))
No. of ways= 15C1 = 15 ways

Case 2: Different students got awards.
No. of ways= 15C2* 2! = 105*2 =210 ways

Total ways= 15+210= 225 ways.

So, I think E. :)
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   26 Feb 2021, 21:27
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Bunuel wrote:
In how many ways can 2 prizes (in Science and Maths) be awarded to 15 students?

A. 190
B. 195
C. 205
D. 210
E. 225

It is not clear from the question whether the prizes are given to one student or two different students. Because the answer would differ, we need to assume either of the possibilities or both together(case in this question).

1. Both prizes can be given to same student.
Ways to award the 1st prize * Ways to award 2nd prize = 15

2. Only one prize is given to one student.
Ways to award the 1st prize * Ways to award 2nd prize = 15 * 14 = 210

210 + 15 = 225

Answer E.
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In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   20 Sep 2021, 22:26
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Is this question poorly written? What are your thoughts? Seems like there might be multiple ways to interpret it...

VeritasKarishma Bunuel chetan2u
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   20 Sep 2021, 23:59
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soondoobu wrote:
Is this question poorly written? What are your thoughts? Seems like there might be multiple ways to interpret it...

VeritasKarishma Bunuel chetan2u


I think the question is fair.

In how many ways can you give away 2 distinct prizes to 15 students?
We are not given that 1 student can get only 1 prize (since they are not ranks 1 and 2. They are prizes in distinct subjects. Same student can get both.)
Also, it is clear that we do not have to give away 2 prizes each in the two subjects because the subjects are mentioned in brackets to clarify only.

Actually the question is just: In how many ways can 2 prizes be awarded to 15 students?
The subject clarification is just to tell us that the prizes are distinct and in subjects, not ranks.

How else would one interpret it, I am not sure.
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink] New post   25 Oct 2022, 06:52
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Re: In how many ways can 2 prizes (in Science and Maths) be awarded to 15 [#permalink]
25 Oct 2022, 06:52
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