A selection is to be made for one post of Senior Manager and two posts of Managers. Among the eight candidates called for the interview, only three are eligible for the post of Senior Manager, while all eight are eligible for the post of Managers.

Consider the following statements:
Statement I: The number of ways to select one Senior Manager from the eligible candidates is 3.
Statement II: The number of ways to select two Managers from the remaining candidates is 21.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

A selection is to be made for one post of Senior Manager and two posts of Managers. Among the eight candidates called for the interview, only three are eligible for the post of Senior Manager, while all eight are eligible for the post of Managers.

Consider the following statements:
Statement I: The number of ways to select one Senior Manager from the eligible candidates is 3.
Statement II: The number of ways to select two Managers from the remaining candidates is 21.

Select the correct answer from below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

3 eligible candidates for Senior Manager = 3C1 = 3.

Statement I is correct.

After selecting 1 Senior Manager (from 3), 7 candidates remain (8 &minus; 1), out of which we choose 2 Managers.
Ways = 7C2 = 21.

Statement II is correct.

Hence, correct option is c.

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