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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 multiplied together. What is the sum of all of the possible distinct products?

 Jun 17, 2021
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The balls are labeled 2, 4 and 8. A ball is picked, the value on the label is recorded and then the ball is returned to the bag. This will be done three times and then the values will be mutiplied. 

 

So tha sample space = {(2,2,2), (2,2,4), (2,4,4), (4,4,4), (2,2,8), (2,8,8), (8,8,8), (2,4,8), (4,8,8), (8,8,4),so on....}         (27 permutations)

 

⇒ Sum of distinct products = (2 × 2 × 2) + (2 × 2 × 4) + (2 × 4 × 4) + (4 × 4 × 4) + (4 × 4 × 8) + (4 × 8 × 8) + (8 × 8 × 8) + (8 × 2 × 2) + (8 × 8 × 2) +(2 × 4 × 8)

                                            = 8 + 16 + 32 + 64 + 128 + 256 + 512 + 32 + 128 + 64

                                            =  1240

 

Sum of all distinct products is 1240. 

 Jun 17, 2021

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