SOLUTION: Ten cards are numbered 1 to 10. Three different cards are selected at random from these cards. What is the probability that the sum of the numbers obtained is at most 9?

Question 856885: Ten cards are numbered 1 to 10. Three different cards are selected at random from these cards. What is the probability that the sum of the numbers obtained is at most 9?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The smallest sum the three can have is 6; 1+2+3 = 6.

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There is only 1 way the sum can be 6, that is 1+2+3=6
There is only 1 way the sum can be 7, that is 1+2+4=7
There are 2 ways the sum can be 8, they are 1+2+5=8 and 1+3+4=8
There are 3 ways the sum can be 9, they are 1+2+6=9, 1+3+5=9, and 2+3+4=9

That's 7 successful ways of getting a sum of 9 or less.

The total number of ways  of getting any sum is C(10,3) = 120 ways.

Probability of a successful sum = , 

(which, incidentally is less than 6% of the time.) 

Edwin

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