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Question 2 How many solutions are there to 1 + 22 +13 + 24 + 25 + 6 = 60 for integers Ii 1.

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Answer #1

Finding this numbr is equvalent to place 60 balls and 5 sticks in a row such that no two sticks are places adjacently (sticks are the + signs and if there are two adjacent + signs then the xi between these + signs will be 0).

SO there are 60 balls so 59 gaps in between them so 5 sticks can be laced in these 59 places in (59 C 5)= 59*58*57*56*55/120= 5006386 ways.

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