Q8. - Algebra 2

Question

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities.

 

Choosing 2 different pizza toppings from a list of 6

Step-by-Step Solution

Answer

The situation is a combination and the number of possibilities is 15. 

Step 1. Given Information.

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.

Step 2. Calculation .

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:

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

Step 3. Conclusion .

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