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Bunuel
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Father John forms a choir from the church attendants. 30 people attend 13 May 2021, 05:30
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35% (medium)

Question Stats:

72% (02:04) correct 28% (02:02) wrong based on 158 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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D
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Nidzo
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Father John forms a choir from the church attendants. 30 people attend 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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Father John forms a choir from the church attendants. 30 people attend 13 May 2021, 12:22
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Nidzo
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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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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Father John forms a choir from the church attendants. 30 people attend 13 May 2021, 14:29
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Christophorus
Nidzo
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.
Show more
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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Father John forms a choir from the church attendants. 30 people attend 13 May 2021, 17:25
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AnirudhaS
Christophorus
Nidzo
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.
Show more

Ah okay. Thank you!
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Father John forms a choir from the church attendants. 30 people attend 14 May 2021, 01:32
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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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Father John forms a choir from the church attendants. 30 people attend 18 Feb 2025, 08:17
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