There are 17 broken lightbulbs in a box of 100 lightbulbs A

There are 17 broken lightbulbs in a box of 100 lightbulbs. A random sample of 3 lightbulbs is chosen without replacement. How many ways are there to choose the sample? How many samples contain no broken lightbulbs? What is the probability that the sample contains no broken lightbulbs? How many samples contain exactly I broken lightbulb? W hat is the probability that the sample contains no more than I broken lightbulb?

Solution

a)

C(100,3)

b)

There are :100-17=83 bulbs not broken

SO,

C(87,3)

c)

C(87,3)/C(100,3)

d)

C(17,1)C(83,2)

e)

C(17,1)C(83,2)+C(83,3)