several teachers invested together in a sandwich and soda pop. they call it the

Question

several teachers invested together in a sandwich and soda pop. they call it the teacher sub shop. they offer custom made sandwiches. you can buy sandwich with the following bases, pastrami turkey roast beef or vegetarian. along with that, they offer four kinds of cheese: monterey jack, cheddar, swiss and american. you can also have mustard, mayonnaise, both or neith. The patrons also get to choose white, wheat, or rye bread, but the rye is not offered with either pastravmi or cheddar, as one of the owners object under the rationale that the cominatons of cheddar and rye or pastrami and rye are gross. a sandwich consist of one base, one cheese if desired condiments if desired, and one bread, how may different types of sandwiches does the shop offer?

Explanation / Answer

There are 3 types of bread = Wheat, white and rye.

There are 4 bases- pastrami, turkey, roast beef and veg

There are a total of 5 choices of cheese (since it is not neccessary, we have have an option of no cheese). So no cheese, montery, cheddar, swiss and American.

there are 4 choices of condiments - mustard, mayo, both, none.

Lets take wheat and white bread.

Choices of bread = 2C1 = 2

Choices of base = 4C1 = 4

Choices of cheese = 5C1 = 5

Choice of condiment = 4C1 = 4

Total possibilities = 2 * 4 * 5 * 4 = 160

Lets take rye. In this one choice of base is reduced, and a cheese is reduced

Choices of bread = 1C1 = 1 (only rye)

Choices of base = 3C1 = 3 (pastrami not included)

Choices of cheese = 4C1 = 4 (cheddar not included)

Choice of condiment = 4C1 = 4

Total possibilities = 1 * 3 * 4 * 4 = 48

Therefore total possible sandwiches = 160 + 48 = 208

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.