Question -
Answer -
Given:
Total number of boys =12
Total number of girls= 10
Total number of girlsfor the competition = 10 + 2 = 12
Number of ways = (no.of ways of selecting 6 boys and 2 girls from remaining 12 boys and 8 girls) + (no.of ways of selecting 5 boys and 3 girls from remaining 12 boys and 8 girls) +(no. of ways of selecting 4 boys and 4 girls from remaining 12 boys and 8girls)
Since, two girls arealready selected,
= (12C6 × 8C2)+ (12C5 × 8C3) + (12C4 × 8C4)
By using the formula,
nCr = n!/r!(n – r)!
= (924 × 28) + (792 ×56) + (495 × 70)
= 25872 + 44352 +34650
= 104874
∴ The total numberof ways of product is 104874 ways.