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In a televised singing competition, at the end of each round the

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RadheyaKulkarni
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In a televised singing competition, at the end of each round the [#permalink] New post   Updated on: 27 Oct 2022, 07:03
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In a televised singing competition, at the end of each round the 3 best performers of the night are invited onto the stage and congratulated. The 2 worst performers of the night are then invited onto the stage before the judges make a final decision on who will be eliminated. How many different combinations of best and worst performers could be invited onto the stage at the end of a round with 8 performers in total?

A. 56
B. 140
C. 560
D. 1020
E. 6720
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C

Originally posted by RadheyaKulkarni on 27 Oct 2022, 00:16.
Last edited by Bunuel on 27 Oct 2022, 07:03, edited 2 times in total.
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In a televised singing competition, at the end of each round the [#permalink] New post   10 Nov 2022, 02:11
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AnujL wrote:
GMATinsight
gmatophobia
KarishmaB
kindly help


Hey AnujL

We have 8 performers, and we need two set of people

1) Top 3 performers
2) Worst 2 performers

The first set, top 3 performers, can be selected in 8C3 ways

Once the three performers are selected, we have five candidates left

Among these five candidates, the second set - worst 2 performers - can be selected in 5C2 ways

Hence total = 8C3 * 5C2 = 560 ways

Note: We can also do the opposite, i.e. select the worst two performers first followed by the best two performers. If we choose to use that logic, the combination would be

8C2 * 6C3 = 560

Hope this helps.
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Re: In a televised singing competition, at the end of each round the [#permalink] New post   27 Oct 2022, 03:05
RadheyaKulkarni wrote:
In a televised singing competition, at the end of each round the 3 best performers of the night are invited onto the stage and congratulated. The 2 worst performers of the night are then invited onto the stage before the judges make a final decision on who will be eliminated. How many different combinations of best and worst performers could be invited onto the stage at the end of a round with 8 performers in total?

A. 56
B. 140
C. 560
D. 1020
E. 6720


Last line of the problem statement suggests that we need different combinations of best, and worst performers, and not the individual combinations of selecting 3 top, and 2 worst. We need combinations of best, and worst together.

since worst, and top contributors together are 5. so out of 8 people, 5 can be selected in 8c5 = 56

hence A.
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Re: In a televised singing competition, at the end of each round the [#permalink] New post   27 Oct 2022, 04:43
even if the question is asking about combinations, isnt ABC winning and DE bottom 2 differnet from ADE and BC (coz winning and losing are different
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Re: In a televised singing competition, at the end of each round the [#permalink] New post   27 Oct 2022, 05:13
respectothers wrote:
even if the question is asking about combinations, isnt ABC winning and DE bottom 2 differnet from ADE and BC (coz winning and losing are different


What you are suggesting is arrangements, and not combinations.
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Re: In a televised singing competition, at the end of each round the [#permalink] New post   27 Oct 2022, 06:34
Bunuel according to Magoosh the Answer is 560. Answer: C. And I couldn't understand the explanation given by Magoosh. I've attached the screenshot. Can someone please explain?
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Screenshot 2022-10-27 at 19.02.15.png
Screenshot 2022-10-27 at 19.02.15.png [ 332.56 KiB | Viewed 1236 times ]

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Re: In a televised singing competition, at the end of each round the [#permalink] New post   10 Nov 2022, 01:46
GMATinsight
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KarishmaB
kindly help
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Re: In a televised singing competition, at the end of each round the [#permalink]
10 Nov 2022, 01:46
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