Question

Question 4 In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Class X1 - Maths -Permutations and Combinations Page 153

Answer 1

3 boys out of 5 boys can be selected in ⁵C₃ ways .
3 girls out of 4 girls can be selected in ⁴C₃ ways .

now,
A/C to concept of fundamental principle of counting,
total number of ways can a team of { 3 boys + 3girls } = ⁵C₃ × ⁴C₃
= 5!/3!×2! × 4!/3!× 1!
[ use the concept of ⁿCₐ =n!/a!(n-a)! ]
= { 5 × 4/2} × { 4 × 3!/3!}
= 5 × 2 × 4
= 40 ways .

Answer 2

Answer:

Step-by-step explanation:

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3 boys out of 5 boys can be selected in =5C3 ways

3 girls out of 4 boys can be selected in =4C3 ways

Number of boys in which 3 boys and 3 girls are selected are

5C3×4C3=5C2×4C1

⇒5×41×2×41

⇒20×42=40

Hence (C) is the correct answer.