A car rental agency at a local airport has available 8 Merce

A car rental agency at a local airport has available 8 Mercedes, 7 BMW, 5 Ford, 3 Toyota and 2 Honda cars. If the agency randomly selects 10 cars, find the probability that a) 2 Mercedes, 2 BMW, 2 Ford, 2 Toyota and 2 Honda are selected. b) 3 Mercedes, 2 BMW, 2 Ford, 1 Toyota and 1 Honda are selected,

Solution

They have 25 cars

so # taking 10 cars = ²⁵C₁₀

(a)# having 2 Mercedes, 2 BMW, 2 Ford, 2 Toyota and 2 Honda

=⁸C₂*⁷C₂*⁵C₂*³C₂*²C₂

so probability = 0.0053965418079027

(b)

# having 3 Mercedes, 2 BMW, 2 Ford, 1 Toyota and 1 Honda

=⁸C₃*⁷C₂*⁵C₂*³C₁*²C₁

so probability = 0.0021586167231611