Answer:
Expected no. of squads = 184755
Step-by-step explanation:
In a party, there are 10 pairs arriving, each consisting of a boy and a girl.
So that means there are 10 boys and 10 girls.
A squad is defined as a collection of boy-girl pairs and one single pair is also a squad on its own.
We are asked to find out the the expected number of squads.
For 10 pairs of boys and girls:
Number of squads = ₁₀C₁₀ × ₁₀C₁₀ = 1 × 1 = 1
For 9 pairs of boys and girls:
Number of squads = ₁₀C₉ × ₁₀C₉ = 10 × 10 = 100
For 8 pairs of boys and girls:
Number of squads = ₁₀C₈ × ₁₀C₈ = 45 × 45 = 2025
For 7 pairs of boys and girls:
Number of squads = ₁₀C₇ × ₁₀C₇ = 120 × 120 = 14400
For 6 pairs of boys and girls:
Number of squads = ₁₀C₆ × ₁₀C₆ = 210 × 210 = 44100
For 5 pairs of boys and girls:
Number of squads = ₁₀C₅ × ₁₀C₅ = 252 × 252 = 63504
For 4 pairs of boys and girls:
Number of squads = ₁₀C₄ × ₁₀C₄ = 210 × 210 = 44100
For 3 pairs of boys and girls:
Number of squads = ₁₀C₃ × ₁₀C₃ = 120 × 120 = 14400
For 2 pairs of boys and girls:
Number of squads = ₁₀C₂ × ₁₀C₂ = 45 × 45 = 2025
For 1 pairs of boys and girls:
Number of squads = ₁₀C₁ × ₁₀C₁ = 10 × 10 = 100
The expected number of squads is
Expected no. of squads = 1 + 100 + 2025 + 14400 + 44100 + 63504 + 44100 + 14400 + 2025 + 100
Expected no. of squads = 184755
