# If a spinner is divided into 8 equal sections and you spin it twice, what is the probability of spinning a sum of 7?

Apr 29, 2018

There is a $\frac{3}{28}$ probability.

#### Explanation:

First, we must determine the possible outcomes of two spinning. This is a long list. Therefore, we can use a formula instead of listing each possibility.

(n!)/((n-r!))

This formula reveals that number of ways $r$ things can be taken from a group of $n$ things. In our problem, we are searching for the number of ways 2 things (for the 2 spins) can be taken from a group of 8 things.

(8!)/((8-2)!) = (8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)= 40320/720=56

Second, we must figure out the different outcomes that will yield a sum of 7. This is a short list, so we don't need to use the formula.

• 4 and 3
• 3 and 4
• 6 and 1
• 1 and 6
• 5 and 2
• 2 and 5

There are six possibilities that total 7.

Therefore, the probability of spinning a sum of 7 is $\frac{6}{56}$ or $\frac{3}{28}$.