1 Shortly after being put into service some buses manufactur

1) Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a particular city has 30 of these buses, and cracks have actually appeared in 9 of them. A quality control inspector selects 5 for visual inspection. How many ways are there to select the buses so that a) exactly 3 have cracks b) none have cracks

Solution

1.

Total buses = 30

buses with cracks = 9

buses without cracks = 21

total buses chose for inspection = 5

exactly three buses have cracks = three buses chose from 9 cracked buses and rest of the two chose from 21 uncracked buses

total ways to chose = (9C3)*(21C2)

= 9*8*7*21*20/(3*2*1*2*1)

= 17640 ways

2.

none of the buses has cracks = buses to chose from 21 uncracked buses

total ways = 21C5

= 21*20*19*18*17/(5*4*3*2*1)

= 20349 ways

let me know if you have any doubt.