Assume a pick-5 lottery is played as follows. Each ticket (panel) has two sets of numbers.
The top half of the panel has numbers 1 through 40.
You must choose 4 distinct numbers out of these, called the White Balls.
The bottome half has numbers 1 through 20.
You must choose 1 number out of these, called the Power-Ball.
Compute each of the following. Show the combinatorial derivation. Show each probabilty in the form 1/x where x is the nearest integer.
(a) Total number of distinct ways to play a ticket.
(b) Probability of winning the Jackpot. (Match all 4 White Balls, and the Power Ball.)
(c) Probability of matching 3 of the White Ball, and the Power Ball.
(d) Probability of matching 3 of the White Balls only.