# 30% of the 20 people in the Math Club have blonde hair. If 3 people are selected at random from the club, what is the probability that none have blonde hair?

##### 1 Answer

#### Explanation:

If we think about it as picking the 3 people simultaneously, then the probability we seek is the chance of picking a group of 3 non-blondes. This is found by dividing the number of groups with 3 non-blondes

#=(14xx13xx12xxcancel(11!))/(cancel(11!)" "cancel(3!))-:(20xx19xx18xxcancel(17!))/(cancel(17!)" "cancel(3!))#

#=(14xx13xx12)/(20xx19xx18)#

#=(7xx13xx1)/(5xx19xx3)" "=" "91/285#

If we think about it as picking the people one by one without replacing them, then the probability of a non-blonde getting picked the first time is

Finally, if we are successful on both the first and second picks, the probability of picking a non-blonde for a third time is, again, the number of non-blondes left (12) divided by the number of people left (18), which gives us

To find the final probability, we multiply these three fractions together:

I hope I helped!