(a) What is a combination of r elements of a set? How many combinations are there of n elements taken r at a time?

(b) How many subsets does a set with n elements have?

(c) A pizza parlor offers ten different toppings. How many three-topping pizzas are possible? How many pizzas are possible?

(a)

To explain:

The combination of r elements, and find the number of combinations of n elements taken r at a time.

Approach:

A combination of r elements from a set is any subset of the set that contains r elements.

If a set has n objects, then the number of combinations of r elements from the set is denoted C(n,r) and is called the number of combinations of n objects taken r at a time is given by,

C(n,r)=n!r!

(b)

To find:

The number of subset does a set with n elements have.

(c)

To find:

The possible number of three topping pizzas, and number of possible pizzas.