Q16. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1. Combination formula.

As the order is not important, combination can be used. The number of combinations of $n$ objects taken $r$ at a time is the quotient of $n!$ and $(n-r)!r!$, that is, $C(n,r)=\frac{n!}{(n-r)!r!}$.

Step 2. Substitution.

Substitute 10 for $n$ and 3 for $r$ into combination formula.

$C(10,3)=\frac{10!}{(10-3)!3!}$

Step 3. Simplify.

Simplify the above obtained expression.

$\begin{array}{l}C(10,3)=\frac{10!}{7!3!}\\ =120\end{array}$

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