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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

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

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