Question

(a): A commitee of 6 members has to be formed from 8 boys and 5 girls . In how many ways can this be done if the committee consist of : (i) Exactly 3 girls , (ii) At least 3 girls?​

Answer 1

Given:

Number of members needed in the committee = 6

Number of boys = 8

Number of girls = 5

To find:

Number of ways of forming the committee with

1. Exactly three girls
2. At least three girls

Solution:

Number of ways of selecting exactly 3 girls = ⁵C₃ = 10

Number of selecting rest of the boys required = ⁸C₃ = 56

Number of ways of forming committee with exactly 3 girls = 10*56 = 560

To select at least 3 girls, number of girls can be 3, 4, or 5

Number of ways of selecting 3 girls = ⁵C₃ = 10

Number of selecting (6-3) boys = ⁸C₃ = 56

Number of ways of forming committee = 10*56 = 560

Number of ways of selecting 4 girls = ⁵C₄ = 5

Number of selecting (6-4) boys = ⁸C₂ = 28

Number of ways of forming committee = 5*28 = 140

Number of ways of selecting 5 girls = ⁵C₅ = 1

Number of selecting (6-5) boys = ⁸C₁ = 8

Number of ways of forming committee = 1*8 = 8

Total number of ways of forming committee = 560 +140 + 8 = 708

Therefore the answers are:

1. 560
2. 708

Answer 2

Answer:

(i) 560

(ii) 780

Step-by-step explanation:

there are 8 boys and 5 girls in total and the committee to be formed are of six member

therefore

(i) so in case of exactly 3 girls

5c3 = 10

and in case of rest of the boys(6-3)

8c3 = 56

so the total ways of forming a committee of 6 members is

10*56 = 560

(ii) now in case of at least three girls there are 3 option . there can be 3, 4 or 5 girls.

so in case of 3 girls

5c3 = 10

and rest of the boys that is (6-3)

8c3 =56

total ways 10*56 =560

in case of four girls

5c4 = 5

and boys (6-4)

8c2 = 28

total ways 5*28 = 140

and in in case of 5 girls

5c5 = 1

rest boys (6-5)

8c1 = 8

total ways 1*8 = 8

so the total ways is 8+140+560 = 780

Thank you

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