Wer +266. A bag contains $3$ balls labeled $2, 4$ and $8$. A ball is to be picked, the value on the label is to be recorded and then the ball is to be returned to the bag. This will be done three times and then the values will be added together. What is the sum of all of the possible distinct sums?

The sum of all the possible distinct sum is 128

Step-by-step explanation:

The number of balls in the bag = 3

The ball labels, (the numbers written on the balls) = 2, 4, and 8

The number of balls selected with replacement = 1

Therefore, we have have, the number of ways of selecting 1 ball from 3 = 3 ways

The distinct combination of the selected balls are;

2, 2, 2 with sum 2 + 2 + 2 = 6

2, 2, 4 with sum 2 + 2 + 4 = 8

2, 2, 8 with sum 2 + 2 + 8 = 12

2, 4, 4 with sum 2 + 4 + 4 = 10

2, 4, 8 with sum 2 + 4 + 8 = 14

2, 8, 8 with sum 2 + 8 + 8 = 18

4, 4, 4 with sum 4 + 4 + 4 = 12

4, 4, 8 with sum 4 + 4 + 8 = 16

8, 8, 4 with sum 8 + 8 + 4 = 20

8, 8. 8 with sum 8 + 8 + 8 = 24

The distinct sums are therefore;

6, 8, 12, 10, 14, 18, 16, 20, 24

The sum of the distinct sum is 6 + 8 + 12 + 10 + 14 + 18 + 16 + 20 + 24 = 128.

4038

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