Question

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A team to represent India in Common Wealth Games 2010 at Delhi is to be formed from amongst 7 female wrestlers, 6 male
wrestlers, 3 female shooters, 2 male shooters, 11 female athletes and 9 male athletes. Q. A team of 10 comprising of 5
males and 5 females can be formed by:
38C10
17C5 x 2105
19P5 x 21P5
add
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BA
0​

Answer 1

Given : A team to represent India in Common Wealth Games 2010 at Delhi is to be formed from amongst 7 female wrestlers, 6 male wrestlers, 3 female shooters, 2 male shooters, 11 female athletes and 9 male athletes

To Find :  A team of 10 comprising of 5 males and 5 females can be formed by:

³⁸C₁₀

¹⁷C₅²¹C₅

¹⁹C₅²¹C₅

Solution:

Females

7 female wrestlers,  3 female shooters 11 female athletes

= 7 + 3 + 11

= 21

5 Females can be selected in ²¹C₅

Males

6 male wrestlers,   2 male shooters,  and 9 male athletes

= 6 + 2 + 9

= 17

5 Males can be selected in  ¹⁷C₅

A team of 10 comprising of 5 males and 5 females can be formed by:

¹⁷C₅²¹C₅

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