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Father John forms a choir from the church attendants. 30 people attend

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Bunuel
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Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   13 May 2021, 05:30
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68% (01:49) correct 32% (02:00) wrong based on 82 sessions
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Father John forms a choir from the church attendants. 30 people attend John's church, and the choir has 28 spots available, with one person as the lead singer. How many different combinations does John have?

A. 3005
B. 4412
C. 6544
D. 12180
E. 24366
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Nidzo
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   13 May 2021, 05:37
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Picking 28 from 30:
30!/28!2!
= 15*29
= 435

From those 28, 1 will be the lead singer so there are 28 possibilities.

435*28 = 12 180

Answer D
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Christophorus
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   13 May 2021, 12:22
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Nidzo wrote:
Picking 28 from 30:
30!/28!2!
= 15*29
= 435

From those 28, 1 will be the lead singer so there are 28 possibilities.

435*28 = 12 180

Answer D



Wait, your process states that there will be 28 diff lead singers. But there are 30 attendants. Shouldn't there be 30 possible lead singers?

I have 30 x 29C27 = 12,180 different combinations but with the possibility that each of the 30 attendants could be the lead singer.
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AnirudhaS
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   13 May 2021, 14:29
Christophorus wrote:
Nidzo wrote:
Picking 28 from 30:
30!/28!2!
= 15*29
= 435

From those 28, 1 will be the lead singer so there are 28 possibilities.

435*28 = 12 180

Answer D



Wait, your process states that there will be 28 diff lead singers. But there are 30 attendants. Shouldn't there be 30 possible lead singers?

I have 30 x 29C27 = 12,180 different combinations but with the possibility that each of the 30 attendants could be the lead singer.

both yours and his processes are correct.
He is choosing 28 out of 30 first.
So technically all 30 can be a lead singer.
After choosing 28 out of 30, he then says there are 28 different possibilities of lead singers out of the chosen 28.

Hope this helps.
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Christophorus
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   13 May 2021, 17:25
AnirudhaS wrote:
Christophorus wrote:
Nidzo wrote:
Picking 28 from 30:
30!/28!2!
= 15*29
= 435

From those 28, 1 will be the lead singer so there are 28 possibilities.

435*28 = 12 180

Answer D



Wait, your process states that there will be 28 diff lead singers. But there are 30 attendants. Shouldn't there be 30 possible lead singers?

I have 30 x 29C27 = 12,180 different combinations but with the possibility that each of the 30 attendants could be the lead singer.

both yours and his processes are correct.
He is choosing 28 out of 30 first.
So technically all 30 can be a lead singer.
After choosing 28 out of 30, he then says there are 28 different possibilities of lead singers out of the chosen 28.

Hope this helps.


Ah okay. Thank you!
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   14 May 2021, 01:32
Expert Reply
Select 1 lead singer from group of 30 = \(^{30}{C_1} = 30\) ways

People left: 29
Spot left: 27

Select 27 spots from 29 \( = ^{29}{C_{27}}= ^{29}{C_{29 - 27}} = ^{29}{C_2} = 29 * 14\) ways

Total ways: \(30 * 29 * 14 = 12,180\)

Answer D
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink] New post   18 Sep 2023, 23:33
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Re: Father John forms a choir from the church attendants. 30 people attend [#permalink]
18 Sep 2023, 23:33
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