We have a box with 8 balls numbered: 0,0,0,1,1,1,2,2 we pick three balls together respectively, what's the prospect that the combination of the numbers of the balls we picked is 5 ?
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Knowing that the balls are shapely matched and we can't see them in the box
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there are 3 balls marked 1 so the total number of ways to get 5 is 3.
There's actually only 1 way to get 5 because we pick up the ball, check out it's number and throw it away
First, you need to find how many ways you can pick 3 balls that add up to 5.
To have a sum of 5 with three balls, you must have the two balls labeled 2.
That adds up to 4.
Then you need a ball labeled 1.
Since there are 3 balls labeled 1, there are 3 ways of picking 3 balls that add up to 5.
Now you need to find how many ways there are of picking 3 balls out of 10 balls.
For the first pick, you can choose from 8 balls.
The second pick is out of 7 balls.
The third pick is out of 6 balls.
There are 8 * 7 * 6 = 336 ways of picking 3 balls.
Of the 336 ways of picking 3 balls, 5 ways result in a sum of 5.
P(sum of 5 with 3 balls) = 5/336
The answer for P(sum of 5 with 3 balls) = 2/8 *1/7 *3/6 *3= 18/336
wanna know why that's the answer ?
Yes, you are correct. You do need 2, 2, 1, but there are 18 ways of arranging those numbers.
Since you need 2, 2, 1, the first 2 is 2 out of 8. The next 2 is 1 out of 7, then the 1 is 3 out of 6. Finally, once you have those picks, you can arrange them in 3 different ways.
2/8 * 1/7 * 3/6 * 3 = 18/336 = 3/56