Respuesta :
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 = ββCββ Γ ββCββ = 1 Γ 1 = 1
For 9 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 10 Γ 10 = 100
For 8 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 45 Γ 45 = 2025
For 7 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 120 Γ 120 = 14400
For 6 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 210 Γ 210 = 44100
For 5 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 252 Γ 252 = 63504
For 4 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 210 Γ 210 = 44100
For 3 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 120 Γ 120 = 14400
For 2 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 45 Γ 45 = 2025
For 1 pairs of boys and girls:
Number of squads = ββCβ Γ ββCβ = 10 Γ 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