Q23. - Algebra 2

Question

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

 

Selecting two of eight employees to attend a business seminar.

Step-by-Step Solution

Answer

The situation is a combination and the number of possibilities is 28. 

Step 1. Given Information.

Given to select two of eight employees to attend a business seminar. 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 employees are just picked and not arranged i.e. the given situation is a combination.

 

Here n=8,r=2

Plugging the values:

 $\begin{array}{l}C\left(8,2\right)=\frac{8!}{\left(8-2\right)!2!}\\ C\left(8,2\right)=\frac{8!}{6!2!}\\ C\left(8,2\right)=\frac{8\cdot 7\cdot 6!}{6!\cdot 2\cdot 1}\\ C\left(8,2\right)=\frac{56}{2}\\ C\left(8,2\right)=28\end{array}$

Step 3. Conclusion .

Hence, the given situation is a combination with 28 possibilities.