SOLUTION: After being put into service, some buses manufactured by a XYZ Company have developed cracks on the underside of the main frame. Suppose a particular province has 23 of these buses

Question 1098383: After being put into service, some buses manufactured by a XYZ Company have developed cracks on the underside of the main frame. Suppose a particular province has 23 of these buses, and cracks have actually appeared in 12 of them.
a. How many ways are there to select a sample of 10 buses from the 23 for a thorough inspection?

b. In how many ways can a sample of 7 buses contain exactly 3 with visible cracks?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
After being put into service, some buses manufactured by a XYZ Company have developed cracks on the underside of the main frame. Suppose a particular province has 23 of these buses, and cracks have actually appeared in 12 of them.
a. How many ways are there to select a sample of 10 buses from the 23 for a thorough inspection?
Combinations of 23, taking 10 at a time = 23x22x21x20x19x18x17x16x15x14 / (10x9x8x7x6x5x4x3x2) = 1144066.

b. In how many ways can a sample of 7 buses contain exactly 3 with visible cracks?
The number of possible samples of 7 buses containing exactly 3 buses with visible cracks is
220 x 330 =7260.
because there are 12 buses with visible cracks,
from which you can make 12x11x10 / (3x2) = 220 different sets,
and there are 23 - 12 = 11 buses without visible cracks,
from which you can make 11X10x9x8 / (4x3x2) = 330 different sets,
so there are 22 x 330 = 7260 ways you can pair one set of each kind to make
a sample of 7 buses containing exactly 3 buses with visible cracks.
RELATED QUESTIONS
The bulbs manufactured by a company (answered by richwmiller)

The Way Bus Company has 140 buses. Each night the buses are parked in a lot. How many... (answered by Alan3354)

A software company has 3 customer service representatives. After a week of observation a... (answered by stanbon)

Hi 60% of the buses in a city are owned by A and the rest by B. When B bought 80 new... (answered by greenestamps)

Sohrab is taking a long walk. He always finds it interesting to see how many sidewalk... (answered by richwmiller)

A bus company recently expanded and no longer has enough room in its garage for all of... (answered by rfer,Edwin McCravy)

Computers manufactured by a certain company have a serial number consisting of a letter... (answered by Fombitz)

Computers manufactured by a certain company have a serial number consisting of a letter... (answered by jim_thompson5910)

computers manufactured by a certain company have a serial number consisting of a letter... (answered by Fombitz)