# A random number generator on a computer selects three integers from 1 to 20. What is the probability that all three numbers are less than or equal to 5?

taylormath | High School Teacher | (Level 2) Adjunct Educator

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Using fractions to represent the probability of each draw.  When the computer choses the first number, the hope is that the number is a number less than or equal to 5.  So for the first draw, there are 5 numbers out of 20 or 5/20 = 1/4.  Since one number has been removed, for the second draw there are only 4 out of 19 or 4/19. For the third draw, the probability becomes 3/18 or 1/6.  All three probabilities are multiplied. The probability that all three numbers are less than or equal to 5 is:

`5/20*4/19*3/18=1/4*4/19*1/6=1/114=.00877` or .877%

Using combinations to figure the probability.

There are 5 numbers that are less than or equal to 5. So there are 5C3 ways to win since three are chosen and order doesn't matter.

There are 20 numbers that are possible choices and the computer chooses 3.  The number of possible ways to draw 3 numbers out of 20 is 20C3.

`(5C3)/(20C3)=10/1140=1/114=.00877=.877%`