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# Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of th

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Two numbers are independently selected from the set of positive integers less than or equal to 5. What is the probability that the sum of the two numbers is greater than their product? Express your answer as a common fraction.

Sep 26, 2019

#1
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To find the probability, first find all possible cases (note that zero is neither positive or negative)

2 are picked out of 5, so

Using the combination formula : $$\frac{5!}{2!3!}$$

Which is - $$10$$

Now that is the number of possible cases of 2 numbers getting chosen out of 5.

Now lets list all the cases of "the sum of the two numbers is greater than their product" (note that one number can't be chosen twice)

1 and 2

1 and 3

1 and 4

1 and 5

And thats all (4 cases)

2/5

Sep 26, 2019

#1
+2

To find the probability, first find all possible cases (note that zero is neither positive or negative)

2 are picked out of 5, so

Using the combination formula : $$\frac{5!}{2!3!}$$

Which is - $$10$$

Now that is the number of possible cases of 2 numbers getting chosen out of 5.

Now lets list all the cases of "the sum of the two numbers is greater than their product" (note that one number can't be chosen twice)

1 and 2

1 and 3

1 and 4

1 and 5

And thats all (4 cases)