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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A team of 7 members is to be selected from 4 boys and 5 girls. Find the number of girls in the team. I) No. of ways of selecting boys is 1. II) No. of ways of selecting girls is 10. III) If one more girl is to be selected, then the no. of girls and boys in the team will become equal.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A team of 7 members is to be selected from 4 boys and 5 girls. Find the number of girls in the team. I) No. of ways of selecting boys is 1. II) No. of ways of selecting girls is 10. III) If one more girl is to be selected, then the no. of girls and boys in the team will become equal. Correct Answer Any one

Let the no. of girls and boys in the team be ‘x’ and ‘y’ respectively

⇒ x + y = 7

Considering statement I,

No. of ways of selecting y out of 4 boys = 1

⇒ 4Cy = 1

We know, 4C4 = 1

⇒ y = 4

Hence, no. of girls = 7 - 4 = 3

Considering statement II,

No. of ways of selecting x out of 5 girls = 10

⇒ 5Cx = 5

We know, 5C2 = 5C3 = 10

If x = 2, y = 7 - 2 = 5, which is not possible as total boys is only 4

If x = 3, y = 7 - 3 = 4, which is possible

Hence, no. of girls = 3

Considering statement III,

When one more girl is selected,

No. of boys = no. of girls

⇒ y = x + 1

But, x + y = 7

⇒ x + x + 1 = 7

⇒ 2x = 6

⇒ x = 3

Hence, no. of girls = 3

∴ The question can be answered using any one of the given statements

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