Probability question: Picking from a group of 5 students

[gmattesttaker2]

Hello,

Can you please tell me if my solution is correct here:

A teacher will pick a group of 5 students out of a group of 5 girls and 5 boys, what
is the probability of picking a group that includes exactly 3 girls?

(This is from GMAT Word Problems book. The answer in the book seems to be wrong.)


My approach is as follows:

P(GGGBB) = (5/10)(4/9)(3/8)(5/7)(4/6)= 5/126

Now we can find the total number of ways to arrange 3 girls and 2 boys using Brent's MISSISSIPPI technique (which Brent has also explained in detail here: https://www.beatthegmat.com/p-c-t274535.html#712266 ):

(5 x 4 x 3 x 2 x 1)/(3! x 2!) = 10

Hence, total number of ways to pick 3 girls and 2 boys = (5/126)(10) = 25/63


Thanks a lot,
Sri

[[email protected]]

Hi Sri,

Yes, your approach is correct. This math can be done in a couple of different ways, so the ultimate question is how long did it take you to come up with this solution. On any given question, remember that you have 2 goals:

1) Get the question correct.
2) Do so in the least amount of time possible (while making sure that you can complete the entire section on time).

GMAT assassins aren't born, they're made,
Rich

[theCodeToGMAT]

5G & 5B

To find; P(3G)

Ways = 5c3 * 5c2 / 10c5

= 5x2 * 5x2 * 5!/ 10x9x8x7x6

= 10 * 10 * 5x4x3x2 / 10x9x8x7x6

= 25/63