Jurors Problem

[tanyasethi]

Twelve jurors must be picked from a pool of n potential jurors. If m of the potential jurors are rejected by the defense counsel and the prosecuting attorney, how many different possibile juries could be picked from the remaining potential jurors?

1) if one less potential juror had been rejected, it would be possibile to create 13 different juries

2) n= m + 12

I know this question has appeared on the forums before, but I can't seem to understand the solution there. Pls help.

The OA is D

[Anurag@Gurome]

Twelve jurors must be picked from a pool of n potential jurors. If m of the potential jurors are rejected by the defense counsel and the prosecuting attorney, how many different possible juries could be picked from the remaining potential jurors?

1) if one less potential juror had been rejected, it would be possible to create 13 different juries
2) n= m + 12/quote]

Number of remaining jurors = (n - m)
Hence, number of different juries = number of ways to select 12 jurors out of (n - m) jurors = (n - m)C12

Hence, we need to determine the value of (n - m)

Statement 1: (n - m + 1)C12 = 13
We can solve the above equation to get the value of (n - m). Or we can simply apply a popular observation about combination formula by which if xCn = (n + 1), then x = (n + 1)

Hence, here, (n - m + 1) = 13 --> (n - m ) = 12

Sufficient

Statement 2: (n - m) = 12

Sufficient

The correct answer is D.

[tanyasethi]

Thank you Anurag! That really helped!

[mirantdon]

+1 for D.

Stat 1 :13C12 = 13 .
Hence it has to be 14C12 SUFFICIENT

Stat 2 ; 12C12 =1 sufficient

hence d