There are 8 boys and 5 girls in a class. If four students are selected at random, what is the probab

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28 Jun 2017 Probability

There are 8 boys and 5 girls in a class. If four students are selected at random, what is the probability that 2 girls and 2 boy are selected?

OPtion

1) 4/13
2) 56/286
3) 56/143
4) 1/10
5) 290/715
6) 56/288
7) 55/143
8) 56/134
9) 40/143
10) None of these

Solution

Total number of ways of selecting 4 students = 13C4
Total number of selecting 2 boys = 8C2
Total number of selecting 2 Girl = 5C2

Probability = (8C2 * 5C2)/13C4 = ((8*7/2)*(5*4/2))/(13*12*11*10/4*3*2)
=> 28*10/715 = 56/143

Correct Option: 3 Best Solution (14)

saranya   7 years AGO

boys =8,girls=5,total=13
method of selecting 4 students out of 13
n(s)=13c4=715
n(e)=8c2*5c2=280
p(e)=n(e)/n(s)=280/715=56/143

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Mukund Manohar   7 years AGO

Required Probability = (8C2 * 5C2)/13C4
= (28 * 10) / 715
= 56/143

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Devendra Marghade   7 years AGO

Total students=8 boys+5 girls= 13
Probability of selecting 2 girls and 2 boys = (5C2 x 8C2)/13C4 = (10x28)/715 = 56/143
Option 3)

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M4 Murali   7 years AGO

Any 4 out of 13 can be selected in 13C4=715 ways
2 boys and 2 girla can be selectes in 8C2x5C2 =280 ways
Probability=280/715=56/143

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Gokul Krishnan   7 years AGO

probability 2 boy and 2 girl=8c2*5c2
total boys and girls =13c4
hence =(8c2*5c2)/13c4
=56/143

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sravan marati's   7 years AGO

eight boys can be choosen in the 8c2 ways =28
five girls can be choosen in the 5c2 ways=10
total probality 13c4=715
now 28*10=280
finally 280/715=56/143

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Navam sharma   7 years AGO

total possibilities is 715(ncr)
favorable are 280
so p=280/715

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Souham Singh   7 years AGO

n(s)=13C4;
n(E)=8C2+5C2;
P(E)=n(e)/n(s);
p(E)=56/143

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meenakshi sundari   7 years AGO

n(s)=sample space
n(s)=13C4=715
N(E)=8C2*5C2=280
P(E)=N(E)/N(S)
280/715=56/143
OPTION 3

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binaya   7 years AGO

n(E)=13C4=13*12*11*10/4!=715
n(S)=8C2*5C2=28*10=280
P(E)=n(E)/n(S)=280/715
=56/143

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S.MUKESH KANNA   7 years AGO

Boys=8
Girls=5
Total=13
No.of students selected =4
Methods of selecting 4 students out of 13

n(s)=13C4
=715

n(e)=8C2×5C2
=280

P(e)= n(e)/n(s)
=280/715
=56/143

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NABA KISHORE PADHY   7 years AGO

The answer is C(8,2)*C(5,2)/C(13,4)
By solving it will be 28*10/715=280/715=56/143

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uday   7 years AGO

probability is no of ways by total ways
(8c2 *5c2 ) / 13c4 =56/143

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Rishav Jha   7 years AGO

total no. of ways to select 4 students =
(8C4 * 5C0) + (8C3*5C1) + (8C2*5C2) + (8C1*5C3) + (8C0*5C4) =715
no. of ways to select 2 boys and 2 girls =
8C2 * 5C2 = 280
therefore required probability = 280/715 = 56/143

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