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02 May 2020, 18:02
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Bunuel
nifoui
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
A: 1/14
B: 1/7
C: 2/7
D: 3/7
E: 1/2
I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.
Will post OA later.
A: 1/14
B: 1/7
C: 2/7
D: 3/7
E: 1/2
I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.
Will post OA later.
P=Favorable outcomes / Total # of outcomes
Favorable outcomes: 2 women and 2 men = \(C^2_5*C^2_3=30\);
Total # of outcomes: 4 people out of 5+3=8 = \(C^4_8=70\);
\(P=\frac{30}{70}=\frac{3}{7}\).
Answer: D.
Bunuel
Should we not divide 30 with 2! as order of the selection does not matter. I'm getting 15/70 or 3/14 as an answer.
20 Jul 2020, 12:15
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KaranB1
Bunuel
nifoui
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
A: 1/14
B: 1/7
C: 2/7
D: 3/7
E: 1/2
I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.
Will post OA later.
A: 1/14
B: 1/7
C: 2/7
D: 3/7
E: 1/2
I find the explanation provided in MGMAT very complicated and would like to know what techniques other people would recommend to solve this problem in 2 mins.
Will post OA later.
P=Favorable outcomes / Total # of outcomes
Favorable outcomes: 2 women and 2 men = \(C^2_5*C^2_3=30\);
Total # of outcomes: 4 people out of 5+3=8 = \(C^4_8=70\);
\(P=\frac{30}{70}=\frac{3}{7}\).
Answer: D.
Bunuel
Should we not divide 30 with 2! as order of the selection does not matter. I'm getting 15/70 or 3/14 as an answer.
Hi KaranB1,
Since the calculation has already used the Combination Formula to determine all of the groups of '2 men' and all of the groups of '2 women', that aspect of the calculation (re: order does NOT matter) has already been accounted for - and you do NOT need to divide by 2!
GMAT assassins aren't born, they're made,
Rich
08 Jun 2021, 04:01
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Solution:
The total number of possibilities of choosing/selecting 4 of 8 people = 8C4
To have exactly 2 women we need 2 men and 2 women in 3C2 and 5C2 ways
=>Number of ways = 3C2 * 5C2 (AND condition)
=30
Probability = 30/70 =3/7 (option d)
Devmitra Sen
GMAT SME
The total number of possibilities of choosing/selecting 4 of 8 people = 8C4
To have exactly 2 women we need 2 men and 2 women in 3C2 and 5C2 ways
=>Number of ways = 3C2 * 5C2 (AND condition)
=30
Probability = 30/70 =3/7 (option d)
Devmitra Sen
GMAT SME
