Question

A committee of four is to be formed from 3 engineers, 4 economist, 2 statistician and 1 chartered accountant. What is the probability that the committee consists of one chartered accountant and at least one economist?

Answer 1

Given that there are in all 3 engineers, 4 economist, 2 statistician and 1 chartered accountant.

Total number of samples n = 10

r = number of random selection

The probability 'P' that the committee of 4 team members consists of one chartered accountant and at least one economist is given by the following sets of possibilities -

Based on various combinations for selection from individual groups we get,

P = $\frac {Total\ no\ of\ favorable\ outcomes\ in\ various\ combinations}{Total\ number \ of\ outcomes}$

P = { {1C1x4C1x3C1x2C1} + {1C1x4C1x3C2x2C0} + {1C1x4C1x3C0x2C2} + {1C1x4C2x3C1x2C0} + {1C1x4C2x3C0x2C1} + {1C1x4C3x3C0x2C0} } / ₁₀C₄

By using the formula for combination _nC_r = $\frac {n!}{r!(n-r)!}$

Substituting the value of probabilities in the above equation we get,

P = 0.35238