1 A) A deli makes sandwiches with 5 different meats, 6 different cheeses, and 8

Question

1 A) A deli makes sandwiches with 5 different meats, 6 different cheeses, and 8 different condiments. How many different sandwiches with just 1 kind of meat, 1 kind of cheese, and 1 condiment can a customer order?

1 B) The deli takes a survey of its customers about which of its 6 cheese varieties are their favorites. In how many ways could the top 3 favorites be chosen in order of popularity?

1 C) Many people coming into the bakery order sandwiches with 3 condiments. How many different sandwiches with 3 condiments (and 1 type of meat, 1 type of cheese) could be created?

Explanation / Answer

(A)
1 kind of meat can be selected in 5C1 = 5 ways
1 kind of cheese can be selected in 6C1 = 6 ways
1 kind of condiment can be selected in 8C1 = 8 ways

Hence possible number of different possible sandwiches are 5 * 6 * 8 = 240

(B)
3 popular cheeses out of 6 can b selected in 6C3 ways = 20

(C)
Three condiments out of 8 can be selected in 8C3 ways = 56
Different possible sandwiches are 5 * 6 * 56 = 1680

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