Question

5.A shipment of 200microwavescontains twentydefective units. In how many ways can a vending company buy fifteenof thesemicrovavesand receivea.No defective units(2pts)b.Exactly two defective units.(2pts)c.At least one defective unit.(2pts)

Answer 1

Explanation:

Total no. of goods, n = 200

no. of defective units in the goods, d = 20

hence the no. of proper units,

g = n-d

g = = 200-20

g = 180

a)

ways in which a vending company buys fifteen of these microwaves and receive no defective units be:

`^(180)C_(15)=(180!)/(15!* (180-15)!)`

`\approx 2.83* 10^(21)`

b)

ways in which a vending company buys fifteen of these microwaves and receive exactly two defective units be:

`^(20)C_2* ^(180)C_(13)=(20!)/(2!* (20-2)!) * (180!)/(13!* (180-13)!)`

`\approx 190* (2.146* 10^(19))`

`\approx 4.076* 10^(21)`

c)

ways in which a vending company buys fifteen of these microwaves and receive at least one defective units be:

`^(20)C_(1)* ^(199)C_(14)=(20!)/(1!* (20-1)!) * (199!)/(13!* (199-13)!)`

`\approx 20* (8.258* 10^(19))`

`\approx 1.652* 10^(21)`