There are 8 people fishing at Lake Connor: 3 have fishing licenses, and 5 do not. An inspector chooses two of the people at random. What is the probabili

Question

There are 8 people fishing at Lake Connor: 3 have fishing licenses, and 5 do not. An inspector chooses two of the people at random. What is the probability that neither person has a license? Write your answer as a fraction in simplest form.

Answer 1

3 have a license, 5 do not have a license

the first choice is 5 out of 8, or 5/8

the second choice is 4 out of 7, or 4/7

(5/8)*(4/7)=20/56=10/28=5/14

another way to look at it is...

how many ways can you choose 2 people out of 8 people ?

8!/2!(8-2)!=8!/2!*6!=8*7/2=56/2=28 ways

how many ways can you choose 2 people out of 5 people ?

5!/2!(5-2)!=5!/2!*3!=5*4/2=20/2=10

10/28=5/14 again

call the 5 people who don't have a license A,B,C,D, and E

how can they be paired together ?

AB,AC,AD,AE,BC,BD,BE,CD,CE, and DE for a total of 10

again 10/28=5/14