Given as
The total boys are = 25
The total girls are = 10
The boat party of 8 to be made from 25 boys and 10 girls, by selecting 5 boys and 3 girls.
Therefore,
On 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
Hence, the total number of different boat parties is 6375600 ways.
