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The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A committee of 5 people is to be formed with 2 female and 3 male trainers. The “talent pool” from where trainers are to be shortlisted has total ‘x’ female and ‘y’ male trainers. The probability of choosing the committee is given as 3/5. What is the total number of trainers in the “talent pool”? I) The number of ways in which 2 trainers can be chosen from the “talent pool” is 15. II) The number of ways 2 female trainers can be chosen from ‘x’ female trainers is 3.

The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A committee of 5 people is to be formed with 2 female and 3 male trainers. The “talent pool” from where trainers are to be shortlisted has total ‘x’ female and ‘y’ male trainers. The probability of choosing the committee is given as 3/5. What is the total number of trainers in the “talent pool”? I) The number of ways in which 2 trainers can be chosen from the “talent pool” is 15. II) The number of ways 2 female trainers can be chosen from ‘x’ female trainers is 3. Correct Answer Either I or II

Let the total no. of trainers be ‘z’ = x + y

Given, probability of choosing the committee = No. of ways of choosing the committee satisfying the conditions/Total no. of ways in which committee can be formed without restriction = 3/5

⇒ 3/5 = (xC2 × yC3)/zC5      ----(1)

From Statement I,

2 trainers can be chosen from the “talent pool” in 15 ways

⇒ (x + y)C2 = 15

⇒ (x + y)!/ = 15

⇒ (x + y)(x + y - 1)/2 = 15

⇒ z(z - 1) = 30

⇒ z = 6

From Statement II,

The number of ways 2 female trainers can be chosen from ‘x’ female trainers is 3

⇒ xC2 = 3

⇒ x!/ = 3

⇒ (x)(x - 1) = 6

⇒ x = 3

‘y’ can be found by substituting x in equation (1)

∴ The question can be answered using either of the statement

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