Question

A restaurant offers its patrons the following choices for a complete dinner:

i. choose one appetizer out of four;

ii. choose one entree out of five;

iii. choose two different items from a list of three kinds of potatoes, three vegetables, and one salad;

iv. choose one dessert out of four;

v. choose one beverage out of three.

a. How many different dinners can be ordered without ordering more than one kind of potato, assuming that no course is omitted?

b. How many different dinners can be ordered with no more than one kind of potato if one item, other than the entree, is omitted?

Answer 1

a)

you can choose one appetizer in 4 ways

You can choose one entree in 5 ways

You can choose either one potato or no , if you choose one patato than you can choose it in 3 ways. Followed by selecting 1 item from three vegetable and one salad, than you can choose it in 4 ways. If you choose no potato than you can choose 2 items from three vegetable and one salad in

You can choose one desert in 4 ways

You can choose one beverage in 3 ways

Total number of different dinner is = 4 * 5 * 3 * 4 * 4 * 3 + 4 * 5 * 6 * 4 * 3 =4320

b) if the appetizer is omitted

Total number of different dinner is = 5 * 3 * 4 * 4 * 3

if the desert is omitted

Total number of different dinner is = 4 * 5 * 3 * 4 * 3

If the beverage is omitted

Total number of different dinner is = 4 * 5 * 3 * 4 * 4

Total number of different dinners can be ordered with no more than one kind of potato if one item, other than the entree, is omitted =5 * 3 * 4 * 4 * 3 + 4 * 5 * 3 * 4 * 3 + 4 * 5 * 3 * 4 * 4=2400