Question

A pizza parlor offers a choice of 15 different topping how many for topping pizza are possible

Answer 1

Given:

Number of choices offered, n = 15

Number of toppings (sample), r = 4

Let's find the number of possible 4-topping pizzas possible.

To solve this exercise, we are to use combination.

Combination involves the arrangement of objects without any repitition of orders of arrangement.

Apply the formula:

$^nC_r=\frac{n!}{r!(n-r)!}$

Thus, we have:

$^{15}C_4=\frac{15!}{4!(15-4)!}$

Solving further:

$\begin{gathered} ^{15}C_4=\frac{15!}{4!(11)!} \\ \\ ^{15}C_4=\frac{15\ast14\ast13\ast12\ast11!}{4\ast3\ast2\ast1\ast11!} \\ \\ ^{15}C_4=\frac{15\ast14\ast13\ast12}{4\ast3\ast2\ast1} \\ \\ ^{15}C_4=\frac{32760}{24} \\ \\ ^{15}C_4=1365 \end{gathered}$

Therefore, there are 1365 possible 4-topping pizzas.

ANSWER:

1365