Question

Please complete two questions using permutation/combination method, thanks.

A builder remodeling a residential kitchen decides to place a splashguard behind the sink consisting of 8 six-inch-square ceramic tiles decorated with different botanical herbs. The tiles will be installed in a custom-made wooden panel. The tile supplier has 12 different herb designs to choose from, and the builder selects 8 of these 12 at random. Suppose the order in which the tiles are arranged on the splashguard does not matter.

A. Two of the 12 herb tiles contain a blue tint that matches the kitchen color scheme. What is the probability that these 2 tiles will be included in the splashguard?

B. The family actually grows 5 of the 12 herbs in a backyard garden. What is the probability that all 5 of these will be included on the splashguard?

Part II:

The Robert F. Kennedy Justice Building in Washington, D.C., contains 68 murals and 35 sculptures. Suppose that during a visitor tour, you are able to see 20 total items (murals and sculptures) at random.

A. What is the probability that a visitor will see 10 murals and 10 sculptures?

B. What is the probability that the visitor will see only murals?

C. What is the probability that the visitor will see all 18 murals depicting the codifiers of law?

D. Suppose it is possible to see some of the 12 physiographic and industrial regions of the national domain panels but still see only 20 total items. What is the probability that the visitor will see all of these panels and murals but no sculptures?

Answer 1

1. From 12 tiles, 8 tiles are selected randomly. A Two of the 12 tiles have a blue tint. So these 2 tiles should be included. And the rest of the 6 tiles should be selected from the remaining 10 tiles. Total number of ways to choose 8 tiles from 12 tiles 12 C₂ . So the required probability beint 25 x 106 12Cq = 0.4242 8. The family grows 5 of the 12 herbs. So these 5 tiles should be included. And the rest of 3 tiles should be selected from the remaining 7 tiles. Ate so the required probability 52₂ X 7 12 Cg Cala ( to Gal).(a = 0.0707

Part II There are 68 murals and 35 Sculptures. So total 68 + 35 = 103 The visitor can See 20 total stems. A The total probability that the visitar 103 C20 can see 20 items The probability that the visitoe will see 10 murals and 10 Sculptures x 35410 = 0.0517 68 C10 103 C20 B. The probability that the visitor sees only murals -5 7.959 x 10 - 68620 103 Cao e. Probability that the visitor see all 18 murals depicting the codifiers of law 18 C18 x 8562 103 C20 3.46 x 10" - 18

but no & Probability that the visitor sees all the 12 panels and murals Sulptures X 68 Cg 6.351 x 10 -13 1292 115C20 Here total items = 68+ 35 + 12 = 115