Question

A committee of 4 people is to be appointed from 3 officers of the production department, 4

officers of the purchase department, 2 officers of the sales department and 1 chartered

accountant. Find the probability of forming the committee in the following manner.

(i) There must be one from each category.

(ii) It should have at least one from the purchase department.

(iii) The charted accountant must be in the committees.

Answer 1

Step-by-step explanation:

A committee of 4 people is to be appointed from 3 officers of the production department, 4

officers of the purchase department, 2 officers of the sales department and 1 chartered

accountant. Find the probability of forming the committee in the following manner.

(i) There must be one from each category.

(ii) It should have at least one from the purchase department.

(iii) The charted accountant must be in the committees.

Answer 2

Given,

A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 chartered accountant.

To Find,

Find the probability of forming the committee in the following manner.

(i) There must be one from each category.

(ii) It should have at least one from the purchase department.

(iii) The charted accountant must be in the committees.

Solution,

(i)P(one from each category) = $\frac{3C1*4C1*2C1*1C1}{10C4}$

                                               = $\frac{3*4*2*1}{210}$

                                               = $\frac{24}{210}$

                                               = 0.14

(ii) P(at least one from the purchase department)

       = 1 - P(None is from purchase department)

       = 1 - $\frac{6C4}{10C4}$

       = 1 - $\frac{15}{210}$

       = $\frac{195}{210}$

       = 0.9286

(iii) P(chartered account in the committees) = $\frac{9C3}{10C4}$

                                                                        = $\frac{84}{210}$

                                                                        = 0.40

Hence, (i)P(one from each category) is 0.14, (ii) P(at least one from the purchase department) is 0.9286 and (iii)P(chartered account in the committees) is 0.40.