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A pizzeria sells small, medium and large pizzas, and offers

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by BTGmoderatorLU » Mon Sep 17, 2018 7:21 pm

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Source: Veritas Prep

A pizzeria sells small, medium, and large pizzas, and offers five different toppings. Its "Three for Thursday" delivery special allows diners to order three one-topping pizzas for the price of one, but with one restriction: all three pizzas must be the same size, and the topping for each pizza must either be the same for all three pizzas or different for each pizza. How many unique orders are available with this special?

A. 25
B. 35
C. 45
D. 55
E. 75

The OA is C.
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by Jay@ManhattanReview » Mon Sep 17, 2018 9:55 pm
BTGmoderatorLU wrote:Source: Veritas Prep

A pizzeria sells small, medium, and large pizzas, and offers five different toppings. Its "Three for Thursday" delivery special allows diners to order three one-topping pizzas for the price of one, but with one restriction: all three pizzas must be the same size, and the topping for each pizza must either be the same for all three pizzas or different for each pizza. How many unique orders are available with this special?

A. 25
B. 35
C. 45
D. 55
E. 75

The OA is C.
Number of sizes available = 3
Number of toppings available = 5

Case 1: Pizzas with the same size and same toppings = 3*5 = 15

Case 2: Pizzas with the same size but with bifferent toppings = 3*5C3 = 3*(5.4.3/1.2.3) = 3*10 = 30
Note that 5C3 is the total number of ways to select 3 toppings out of 5 available toppings

Total number of orders = 15 + 30 = 45

The correct answer: C

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Wed Sep 19, 2018 5:08 pm
BTGmoderatorLU wrote:Source: Veritas Prep

A pizzeria sells small, medium, and large pizzas, and offers five different toppings. Its "Three for Thursday" delivery special allows diners to order three one-topping pizzas for the price of one, but with one restriction: all three pizzas must be the same size, and the topping for each pizza must either be the same for all three pizzas or different for each pizza. How many unique orders are available with this special?

A. 25
B. 35
C. 45
D. 55
E. 75
Since the 3 pizzas in the special must be the same size, we can determine the number of ways the special consists of all small pizzas first and then multiply that result by 3 (since the pizzas could be also medium or large).

If the 3 small pizzas have the same topping, then there are 5 ways to order them since there are 5 different toppings. If the 3 small pizzas have different toppings, then there are 5C3 = (5 x 4 x 3)/(3 x 2) = 10 ways to order them.

Therefore, there are 5 + 10 = 15 ways to order the 3 small pizzas and 15 x 3 = 45 ways to order 3 same-sized pizzas.

Answer: C

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