SOLUTION: there are 3 judges, judging a sporting event. Each of these judges holds up a number, either 1 or a 2 or a 3. The sum of these numbers is the athletes's score.how many different sc

Question 1011714: there are 3 judges, judging a sporting event. Each of these judges holds up a number, either 1 or a 2 or a 3. The sum of these numbers is the athletes's score.how many different scores are possible?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
There are 3 judges, judging a sporting event. Each of these judges holds up a number, either 1 or a 2 or a 3. The sum of these numbers is the athletes's score.how many different scores are possible?

Solution:
The minimum score is 1+1+1=3
The maximum score is 3+3+3=9

We need to examine if all numbers in-between are possible:
At the start, if all judges give a score of one, the total score is 3.
If each judge changes her mind and increase the score by one, we get 4,5,and 6.
The same process can be repeated to get 7,8,9.
So the total possible number of scores is (9-3)+1=7
following added to clarify answer:
The set of possible scores is {3,4,5,6,7,8,9} which gives 7 distinct scores.

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