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In a team of 23 members, there are 14 members which age below 30 years. 7 of the total members attended a conference. What is the probability that the members who attended the conference should consist 2 members of below the age of 30 and 1 member of above the age of 30?

A. \(241513 \over245157\)

B. \(1 \over 2\)

C. \(242513 \over 245157\)

D. \(240513 \over 245157\)


1. Only A
2. Only B
3. Only C 
4. Only D

1 Answer

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Best answer
Correct Answer - Option 4 : Only D

Given:

Total members: 23

Members who age below 30: 14

Formula used:

nCr = n!/((n-r)! × r!)

P = (Number of favorable outcomes)/(Total number if outcomes)

Calculation:

Members who age above 30: 23 - 14 = 9

Probability of members who attended the conference consist 2 members of below the age of 30 and 1 of above the age of 30:

\((14C2 \times 9C5) +(14C3 \times 9C4) + (14C4 \times9C3) + (14C5 \times9C2) + (14C6 \times9C1)\)

=\((91\times126)+(364\times126)+(1001\times84)+(2002\times36)+(3003\times9)\)

\(11466+45864+84084+72072+27027\)

\(240513\)

Total possible combination:

\(23C7 = 245157\)

Probability = \(240513 \over245157\)

∴ Only D is the correct answer.

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