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.?

Option 4 : 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)