Question -
Answer -
Given:
Total boys are = 25
Total girls are = 10
Boat party of 8 to bemade from 25 boys and 10 girls, by selecting 5 boys and 3 girls.
So,
By using the formula,
nCr = n!/r!(n – r)!
25C5 × 10C3 =25!/5!(25 – 5)! × 10!/3!(10-3)!
= 25! / (5! 20!) ×10!/(3! 7!)
=[25×24×23×22×21×20!]/(5! 20!) × [10×9×8×7!]/(7! 3!)
= [25×24×23×22×21]/5!× [10×9×8]/(3!)
=[25×24×23×22×21]/(5×4×3×2×1) × [10×9×8]/(3×2×1)
= 5×2×23×11×21 × 5×3×8
= 53130 × 120
= 6375600
∴ The total numberof different boat parties is 6375600 ways.