from the set 1,2,3,4,5 Doug will choose three distinct numbers and Regina will choose three distinct numbers. What is the probability that Doug and Regina will choose exactly two of the same numbers as each other? Express answer as a common fraction.
Let Doug choose his three first.
How many ways can Regina pick hers up. 5*4*3=60
How many ways can Regina pick the first 2 the same and the 3rd diff from Doug 3*2*2=8
But the different one can be picked up 1st 2nd or 3rd so that is 8*3=24
So i think the prob is 24/60 = 2/5