a lot of 100 bulbs from manufacturing process is known to contain 10 defective and 90 nondefective bulbs. if a sample of 8 bulbs is selected at random what is the probability that the sample has 3 defective and 5 nondefective bulbs

Dear Student,

Given : Total number of bulbs in the lot    =  10 Defective +  90 Non-Defective =  100

Number of bulbs selected = 8

We know formula for probability :

Probability P ( E )  =

And Selecting 8 bulbs from the lot

Total No. of Possible Choices =  Number of ways in which the 8 bulbs can be selected from the total 100 bulbs = n ( S ) = 100C8
So,
n ( S ) =

And
Sample of 8 bulbs is selected at random and the sample has 3 defective and 5 non defective bulbs , So

n ( E ) = 10C3 $×$ 90C5  =

Therefore,

Probability that the sample has 3 defective and 5 non defective bulbs =