SOLUTION: What is your probability of winning the lottery if the balls number 1 to 54 and you have to get correct? The order in which the selection is made dont matter..

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Question 88973: What is your probability of winning the lottery if the balls number 1 to 54 and you have to get correct? The order in which the selection is made dont matter..
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You didn't say how many balls are selected. Lets say you choose 5 balls, and since order doesn't matter, we can use the combination formula:



Start with the given formula

Plug in n=54 and r=5

Subtract 54-5 to get 49

= Expand 54!

= Expand 49!

= Cancel like terms


=%2854%2A53%2A52%2A51%2A50%29%2F5%21%29 Simplify

Calculate 54*53*52*51*50 to get 379,501,200

Calculate 5! to get 120


Multiply the values in the denominator


Divide

So 54 choose 5 (where order does not matter) yields 3,162,510 unique combinations


So the probability of winning is 1%2F3162510