An urn contains a red and b green balls.We select k balls without replacement with k ≤ min{a, b}. Show that the probability all selected balls are of the same color equals

(a)k + (b)k

(a + b)k

.

Application: In a lottery with 49 numbers, 6 are selected in each draw. Find the probability that, in a particular draw, all six winning numbers are

(i) even;

(ii) odd.