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.