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Chapter 12: Q16. (page 797)

PIZZA how many ways can 3 different toppings be chosen from a list of 10 toppings?

Short Answer

Expert verified

There are 120 ways in which 3 different toppings can be chosen from a list of 10 toppings.

Step by step solution

01

Step 1. Combination formula.

As the order is not important, combination can be used. The number of combinations ofn objects takenr at a time is the quotient ofn! and (n−r)!r!, that is, C(n,r)=n!(n−r)!r!.

02

Step 2. Substitution.

Substitute 10 for n and 3 forr into combination formula.

C(10,3)=10!(10−3)!3!

03

Step 3. Simplify.

Simplify the above obtained expression.

C(10,3)=10!7!3!=120

Therefore, there are 120 ways in which 3 different toppings can be chosen from a list of 10 toppings.

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