Question

A shipment of 10 microwaves contains 3 defective units. In how many ways can a vending company purchase 4 of these units and receive (a) all good units (b) two good units and (c) at least two good units?

Answer 1

Out of 10 units of microwave there are 7 good units and 3 defective units.

(a)The number ways of receiving all 4 units perchased by the vending company to be good ones are
`""^7C_4=(7!)/(3!xx4!)=35`

(b)The number ways of receiving 2 good units out of 4 units perchased by the vending company are
`""^7C_2xx""^3C_2=(7!)/(2!xx5!)xx(3!)/(2!xx1!)=63`

(c)The number ways of receiving at least 2 good units out of 4 units perchased by the vending company are
#""^7C_2xx""^3C_2 +""^7C_3xx""^3C_1+ ""^7C_4#

#=(7!)/(2!xx5!)xx(3!)/(2!xx1!)+(7!)/(4!xx3!)xx(3!)/(2!xx1!) + (7!)/(3!xx4!) #

`=63+105+35=203`