A group contains 7 boys and some girls. The number of teams of 5

Question

A group contains 7 boys and some girls. The number of teams of 5 comprising 3 boys and 2 girls is 525. How many girls are in the group?

A. 5
B. 6
C. 7
D. 9
E. 11

Rabab36 · Answer

7C3*nC2=525
solving we get 
n=6

option B correct

mysterymanrog · Answer

7 boys, x number of girls. 
We are told there are 525 combinations for a team of 3 boys, and 2 girls. 
Therefore:

7Choose3*xChoose2=525

7choose3=7!/(4!*3!)=35
xChoose2 can be written as x(x-1)/2!

35*x(x-1)/2!=525
x(x-1)=30

Rather than solve the quadratic, you can simply plug in answer choices. x=6 clearly works, so there are 6 girls in the group.

gmatophobia · Answer

Let the number of girls = n

7C_3 * nC_2 = 525

We can factorize 525 and cancel out the terms. This will help speed the calculation.

\frac{7 * 6 * 5 }{ 3 * 2} * \frac{n(n-1) }{ 2} = 5^2 * 7 * 3

n(n-1) = 6 * 5

n = 6

Option B

Prep Toolkit