In the pick4 lottery 4 digits are drawn randomly in order dr

In the pick-4 lottery, 4 digits are drawn randomly in order (drawing 1355 is not the same as drawing 1535). You buy one ticket. Determine the probability that:
a. You win the jackpot.
b. All but your first digit matches the winning four digit number.
c. Exactly three of your four digits matches those of the winning four digit number.
d. At least three of your four digits match those of the winning four digit number.

Solution

The sample space consists of all tickets with numbers from 0000 to 9999. There are 10,000 of them.

a) 1/10,000

b) First digit can be any of 9 numbers: 9/10,000

c) Exactly three matches = first or second or third or fourth digit can be any of 9 numbers: 4*(9/10000) =36/10,000

d) At least three matches = exactly three or exactly four: (36+1)/10,000=37/10,000