At Pete\'s Pizza Parlor, pizzas come in four sizes: small, medium, large, and co

Question

At Pete's Pizza Parlor, pizzas come in four sizes: small, medium, large, and colossal. A customer can order a plain cheese pizza or request any combination of the following additional seven ingredients: anchovies, green peppers, mushrooms, olives, onions, pepperoni, and sausage. Determine the number of different pizzas that: a) are large or colossal and have exactly four different additional ingredients. b) have exactly three different additional ingredients. e) have exactly three additional ingredients, and they can choose the same ingredient multiple times (for example double pepperoni and single mushrooms).

Explanation / Answer

(a) Choosing exactly 4 ingredients from 7 = 7C4 = 35

Choosing exactly 4 ingredients from 7 for large or colossal = 2*7C4 = 2*35 =70 (ans)

(b) Choosing exactly 3 ingredients from 7 = 7C3 = 35

Since there are four different sizes (small, medium, large, colossal) of pizzas, so answer will be = 4*7C3 = 4*35 = 140 (ans)

(c) Choosing exactly 3 different ingredients from 7 = 7C3 = 35

Choosing exactly 3 ingredients (1 ingredient twice and another once) from 7 = 7C1 * 6C1 = 7*6 = 42

Choosing exactly 3 ingredients (1 ingredient thrice) from 7 = 7C1 = 7

so total is 7C3 + 7C1 * 6C1 + 7C1 = 35 + 42 + 7 = 84

Since there are four different sizes (small, medium, large, colossal) of pizzas, so answer will be = 4*84 = 336 (ans)

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