Question

4. The manager of a large store that sells TV sets wants to set up a display of all the different TV sets that they sell. The manager has seven different TVs that have screen sizes between

37 and 43 inches, nine that have screen sizes between 46 and 52 inches, and twelve that have screen sizes of 55 inches or greater.
a. In how many ways can the manager arrange the 37- to 43-inch TV sets?
b. In how many ways can the manager arrange the 55-inch or greater TV sets?
c. In how many ways can the manager arrange all the TV sets if he is concerned about the order they were placed in?

Answer 1

a. 5040 ways

b. 479001600 ways

c. 3.048883446*10²⁹ ways

Explanation:

The problem is a permutation problem, where
`P = n!`

37 - 43 inches TV = 7

46 - 52 inches TV = 9

Greater than 55 inches TV = 12

Total TV = 7 + 9 + 12 = 28

a) Arranging the 37 - 43 inches TV ( n = 7)

`P = n!\\P = 7!\\P = 7 *6 * 5* 4 * 3 *2 * 1\\P = 5040`

b) Arranging the greater than 55 inches TV ( n = 12)

`P = n!\\P = 12!\\P =12*11*10*9*8 *7 *6 * 5* 4 * 3 *2 * 1\\P = 479001600`

c) Arranging all the TV ( n = 28)

`P = n!\\P = 28!\\P =28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8 *7 *6 * 5* 4 * 3 *2 * 1\\P = 3.048883446*10^(29)`