+586 Two distinct integers, x and y, are randomly chosen from the set {1,2,3,4,5,6,7,8,9,10}. What is the probability that xy-x-y is even?
+129899 If x is odd and y is odd then
(odd) (odd) - (odd) - (odd) =
odd - odd - odd =
even - odd =
odd
If x is odd and y is even then
(odd)(even) - odd -even =
even - odd - even =
odd - even =
odd
So... xy - x - y will only be even when x,y are even
We have these possible even pairs
2,4 4,6 6, 8 8,10
2,6 4,8 6.10
2,8 4,10
2,10
So 10 pairs produce an even result for xy - x- y
And the number of possible pairs is C(10,2) = 45
So....the probability that xy - x - y is even = 10 / 45 = 2 / 9
