Question

(10) A trekking group is to be formed having 6 members. They are
to be selected from 3 girls, 4 boys and 5 teachers. In how many
ways can the group be formed so that there are 3 teachers and 3
boys or 2 girls and 4 teachers?​

Answer 1

Answer:

It's not possible to calculate

Answer 2

The answer is 55 ways

GIVEN

A trekking group is to be formed having 6 members. They are to be selected from 3 girls, 4 boys and 5 teachers.

TO FIND

In how many ways can the group be formed so that there are 3 teachers and 3 boys or 2 girls and 4 teachers?

SOLUTION

The above problem can be simply solved as follows;

3 teachers and 3 boys and 2 girls and 4 teachers means - (3T × 3B) + (2G + 4T)

Ways in which 3 teachers can be selected

= ⁵C₃ = 5!/(3!2!) = 10

Ways in which 3 boys out of 4 can be selected = ⁴C₃ = 4!/(3!1!) = 4

Ways in which 2 girls out of 3 can be selected = ³C₂ = 3!/2!1! = 3

4 teachers out of 5 = ⁵C₄ = 5!/4!1! = 5

Total ways = (10 × 4) + (3×5) = 40 + 15 = 55

Hence, The answer is 55 ways

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