A local lottery is found by randomly selecting 6 pingpong Ba

A local lottery is found by randomly selecting 6 ping-pong Balls from a container in order and without replacement. There are 30 ping pong balls in the container numbered 0 through 29

how many tickets should you buy to give yourself a 1% chance of winning the lottery? then a 10% chance?

Solution

total number of ways of picking 6 ping pong balls from 30 = 30C6

and of all combinations only one way of picking 6 balls is the correct number

probability of a random 6 digit number winning = 1/30C6 = 1/593775

so ,

number of tickets one should buy = 1% * 593775 = 5938 tickets

number of tickets one should buy for 10% chance = 10% * 593775 = 58378 tickets