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Father John forms a choir from the church attendants.

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Father John forms a choir from the church attendants.

by BTGmoderatorLU » Fri Feb 01, 2019 2:52 pm

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Source: Economist GMAT

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

The OA is D
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by [email protected] » Sat Feb 02, 2019 11:20 am
Hi All,

We're told that 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. We're asked for the number of different combinations for the choir. This question involves the Combination Formula, but it also includes a Number Property that can help you to avoid almost all of the 'math' involved:

For the lead singer, we have 30 people to choose from --> 30 possibilities.

Once the lead singer is chosen, we have 29 people for the remaining 27 spots --> 29c27 = (29!)/(27!)(2!) = (29)(28)/2 = (29)(14)

Thus, the total number of possible choirs is (30)(29)(14). Rather than do all of that math though, notice how we will be multiplying by 30; this means that the product will END in a '0'... and there's only one answer that fits that pattern.

Final Answer: D

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by Scott@TargetTestPrep » Wed Feb 06, 2019 6:25 pm
BTGmoderatorLU wrote:Source: Economist GMAT

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

The OA is D
We can have any one of 30 people vie for the lead singer spot, and the remaining 29 people vie for the remaining 27 spots. Therefore, we can have a total of

30C1 x 29C27 = 30 x 29C2 = 30 x (29 x 28)/2 = 12,180 combinations

Answer: D

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edited

by deloitte247 » Thu Feb 07, 2019 7:54 am
Father John forms a choir from the church attendants
30 people attend the church and choir has 28 spots available with one person as the lead singer.
For the lead singer, we have 30 people to start from. once the lead singer has been chosen, we will have to fill the remaining 27 spots from 29 people that are left. $$29C_{27}=\frac{\left(29!\right)}{\left(27!\right)\left(2!\right)}=\frac{\left(29\cdot28\right)}{2}=29\cdot14=406$$
Father now has a total of (406*30) = 12180 different combinations.

$$answer\ is\ option\ D$$
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