91Ó°ÊÓ

Given to choose 2 different pizza toppings from a list of 6. It is to be determined if the situation involves a permutation or a combination and then the number of possibilities are to be calculated.

A permutation is when n objects are available and r are to be picked and arranged in a certain order and the number of permutations is given by$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

A combination is when n objects are available and r are to be picked without arrangement and the number of combinations is given by$C\left(n,r\right)=\frac{n!}{\left(n-r\right)!r!}$

Here, the order of choosing doesn’t affect the final outcome. Hence the toppings are just picked and not arranged i.e. the given situation is a combination.

Here n=6,r=2

Plugging the values:

$\begin{array}{l}C\left(6,2\right)=\frac{6!}{\left(6−2\right)!2!}\\ C\left(6,2\right)=\frac{6!}{4!2!}\\ C\left(6,2\right)=\frac{6â‹\dots 5â‹\dots 4!}{4!â‹\dots 2â‹\dots 1}\\ C\left(6,2\right)=\frac{30}{2}\\ C\left(6,2\right)=15\end{array}$

Hence, the given situation is a combination with 15 possibilities.