The following question has three statements. Study the question and the statements to decide which of the statement(s) is/are necessary to answer the question. A committee having 2 Hindi teachers and 2 English teachers is to be formed from some ‘Hindi teachers’ and ‘English teachers’. The probability of doing so is 3/5. Find the total number of Hindi and English teachers. Statement I: Number of ways to choose 2 teachers out of total teachers is 15 Statement II: Number of ways to choose 2 Hindi teachers out of total Hindi teachers is 3 Statement III: Number of English teachers is 3 Correct Answer Each of the statements alone is sufficient Let the number of Hindi and English teachers is ‘H’ and ‘E’ respectively A committee having 2 Hindi teachers and 2 English teachers is to be formed from H ‘Hindi teachers’ and E ‘English teachers’. The probability of doing so is 3/5 ⇒ (HC2 × EC2)/(H + E)C4 = 3/5 ---- (1) We need to find total number of Hindi and English teachers i.e. (H + E) Statement I: Number of ways to choose 2 teachers out of total teachers is 15 ⇒ (H + E)C2 = 15 ⇒ /2! = 15 Suppose (H + E) = x ⇒ x (x - 1) = 30 Now, Product of two consecutive numbers is given as 30 (6 × 5) so, x = 6 ⇒ (H + E) = 6 Statement (I) alone is sufficient to answer the question Statement II: Number of ways to choose 2 Hindi teachers out of total Hindi teachers is given by 3 ⇒ HC2 = 3 ⇒ H (H - 1) = 6 Now, Product of two consecutive numbers is given as 6 (3 × 2) so H = 3 From equation 1, we can find the value of E also Statement (II) alone is sufficient to answer the question Statement III: Number of English teachers is 3 As, E = 3, value of H can be found from equation 1 Statement (III) alone is sufficient ∴ Each of the statements alone is sufficient to answer the question