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Three different numbers are randomly selected from among the first ten positive integers.  Find the probability that the sum of these three numbers is 15.

 Dec 12, 2019
 #1
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There are a total of 10*9*8 or 720. Lets see what 3 numbers sum up to 15. 

We have the following:

1 6 8 gives us 6 ways.

1 5 9 gives us 6 ways.

1 4 10 gives us 6 ways.

2 6 7 gives us 6 ways.

2 5 8 gives us 6 ways.

2 4 9 gives us 6 ways.

2 3 10 gives us 6 ways.

3 4 8 gives us 6 ways.

3 5 7 gives us 6 ways.

4 5 6 gives us 6 ways.

Adding up the possible ways we get 60 ways.

60/720 is 1/12.

 Dec 12, 2019
 #2
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The 10 numbers are 0 to 9 !!. You can't add 1 + 4 + 10 or 2 + 3 + 10.

 Dec 12, 2019
 #3
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Here are the 60 numbers:

 

069  078  087  096  159  168  186  195  249  258  267  276  285  294  348  357  375  384  429  438  456  465  483  492  519  528  537  546  564  573  582  591  609  618  627  645  654  672  681  690  708  726  735  753  762  780  807  816  825  834  843  852  861  870  906  915  924  942  951  960  Total =  60

Guest Dec 12, 2019

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