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(a) Your restaurant sells t-shirts in several different colors with the restaura

ID: 3151600 • Letter: #

Question

(a) Your restaurant sells t-shirts in several different colors with the restaurant’s name on the front. How many different straight line arrangements can you make in the display case if you have 5 black, 3 white, and 6 red t-shirts to display? (Hint: Use Permutation of Nondistinct Items)

(b) Your restaurant also makes submarine sandwiches. Customers have a choice of 3 different types of bread, 6 different meat combinations, and 5 different kinds of cheese for their sandwich. How many different sandwiches can a customer order?

(c) A local artists brings you 15 of her paintings to hang on the walls of your restaurant. You only have space for 4 of them. How many different ways can you choose 4 paintings to hang on the walls if the order of the paintings doesn’t matter?

(d) A chalkboard just outside the front door of your restaurant is used to advertise the nightly specials. Tonight the restaurant is featuring 7 specials. How many different ways can the 7 specials be listed on the chalkboard?


(e) Just for fun you are going to randomly select 4 toppings for tonight’s mystery pizza special. You have 25 different toppings to choose from. How many pizzas are possible if you can only choose 4 different toppings for the special?

What is the probability that you choose a pizza with mushroom, avocado, bacon, and anchovy pizza or a pizza with onion, apple, garlic, and bbq chicken pizza? (Hint: You are choosing 2 pizzas from however many different pizzas with 4 topping combinations are possible for you to choose from.) (Round 5 decimals)

Explanation / Answer

(a) Your restaurant sells t-shirts in several different colors with the restaurant’s name on the front. How many different straight line arrangements can you make in the display case if you have 5 black, 3 white, and 6 red t-shirts to display? (Hint: Use Permutation of Nondistinct Items)

Note that for Permutation of Nondistinct Items, we have

#ways = N!/(n1! n2! n3!...)

where

N = total items = 5+3+6 = 14

n1 = 5 black

n2 = 3 white

n3 = 6 red

Hence,

#ways = 14!/(5!3!6!) = 168168 ways [ANSWER]

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