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Manager  S
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

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6 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:42) correct 35% (02:45) wrong based on 81 sessions

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Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

$$A) \frac{1}{33}$$
$$B) \frac{15}{33}$$
$$C) \frac{23}{66}$$
$$D) \frac{12}{33}$$
$$E) \frac{1}{3}$$

Posted from my mobile device

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Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas
Senior Manager  V
Joined: 22 Feb 2018
Posts: 415
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

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hasnain3047 wrote:
Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

$$A) \frac{1}{33}$$
$$B) \frac{15}{33}$$
$$C) \frac{23}{66}$$
$$D) \frac{12}{33}$$
$$E) \frac{1}{3}$$

Posted from my mobile device

OA: C

Total Number of case of selecting four students out of 11 $$= C(11,4) = \frac{11!}{7!4!}=330$$

Number of ways of selecting 4 girls or 3 girls and 1 boy to form a 4 member team $$= C(6,4)*1 + C(6,3)*C(5,1)=\frac{6!}{4!2!}*1 +\frac{6!}{3!3!}*\frac{5!}{4!1!}=115$$

Required probability $$= \frac{115}{330} =\frac{23}{66}$$
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3142
Re: Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

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2

Solution

Given:
• Out of 5 boys and 6 girls, 4 students are selected at random.

To find:
• The probability that selection has more number of girls than the number of boys.

Approach and Working:
From 11 students, 4 can be selected in $$^{11}C_4$$ = 330 ways

Now, if number of girls are more than boys, then the possible cases are:
• 3 girls and 1 boy = $$^6C_3$$ x $$^5C_1$$ = 20 x 5 = 100
• 4 girls and 0 boy = $$^6C_4$$ = 15
• Hence, the probability = $$\frac{100+15}{330} = \frac{115}{330} = \frac{23}{66}$$

Hence, the correct answer is option C.

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Director  G
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

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hasnain3047 wrote:
Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

$$A) \frac{1}{33}$$
$$B) \frac{15}{33}$$
$$C) \frac{23}{66}$$
$$D) \frac{12}{33}$$
$$E) \frac{1}{3}$$

Posted from my mobile device

more number of girls than boys is possible in 2 cases

1. 3 girls and 1 boy = $$\frac{6c3*5}{11c4}$$
2. all 4 girls = $$\frac{6c4}{11c4}$$

= $$\frac{115}{330}$$ =$$\frac{23}{66}$$ Out of 5 boys and 6 girls, 4 students are sellected at rando   [#permalink] 28 Aug 2018, 01:32
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