A game at the fair involves ping-pong balls numbered 1 to 18. You can win a prize if you correctly choose the 5 numbers that are randomly drawn.

Question

A game at the fair involves ping-pong balls numbered 1 to 18. You can win a prize if you correctly choose the 5 numbers that are randomly drawn. What are your chances of winning?

Answer 1

You can solve this using the "slot method".  First, figure out how many slots to fill.  Since 5 balls will be drawn, there are 5 slots.  Then fill each slot with the number of balls that could possibly be there.  There are 18 possibilities for the first ball drawn, so put 18 in the first slot.  There are only 17 possibilities for the second ball drawn, so put 17 in the second slot.  Likewise put 16 in the third slot, 15 in the fourth slot, and 14 in the fifth slot.  Now that the slots are full, multiply them together.

 

18 x 17 x 16 x 15 x 14 = 1028160

 

So there are 1,028,160 possible 5 ball combinations that could be drawn, so your chances of picking those exact balls are 1 in 1,028,160!  Don't lose all your money on it.

Answer 2

5/18*4/17*3/16*2/15*1/14 = 120/1028160 = 1/8568