A shipment of 25 flat screen televisions contains three defective units. In how many ways can a vending company purchase four of these units and receive the following?

Question

a) all good units

_____ ways

b) two good units

_____ ways

c) at least two good units

_____ ways

Answer 1

Assuming random selection, no prior knowledge, order does not matter.

a) 22*21*20*19 or ₂₂ C ₄ - which is 7315 (note: total combinations , good or bad would be ₂₅ C ₄ or 12650 )

b) 2 bad units ( 3*2 or ₃ C ₂ - 3) times 2 good units ( 22*21 or ₂₂C₂ - 231) or 693

c) Same as asking how many ways to get 2 or less bad units. That would be 0 bad units (answer to a) plus 2 bad units (answer b) , plus 1 bad unit ( ₃C₁ * ₂₂C₃ or 1543), which together equal 9551