suppose a company manufactures four different items A B C an

suppose a company manufactures four different items A, B, C, and D. the company wants to have two television advertisements showing one item on each show. Answer the following questions:

a) from how many possibilities can the company chooses the items?

b) how many of the ways involve the same item being used?

c) what fraction of the ways involves the same item being used?

Solution

a) from how many possibilities can the company chooses the items?

-> First advertisement can show 4 items and second advertisement can also show 4 items. Thus a total of 4*4 = 16 possibilities are there in choosing items.

b) how many of the ways involve the same item being used?

-> Number of ways in which only different items are used will be C(4,2) = 6.

Number of ways involving the same item being used = 16-6 = 10.

c) what fraction of the ways involves the same item being used?

-> fraction of ways involving the same item being used = 10/16 = 0.625