4 octagonal die(faces 1-8) are thrown together. what is the total number of ways in which the sum of the numbers obtained  on the dice is 25??

Let the numbers obtained in the four tries be a, b, c and d.
Therefore, we need to find the number of natural number solutions of the equation

a+b+c+d = 25 where 1<= a,b,c and d =< 8

Let e = 8 - a; f = 8 - b; g = 8 - c and h = 8 - d

Therefore, e+f+g+h = 7 and 0<=e,f,g,h=<7

The number of natural number equations to the above equation is (7+3)C3 = 120 which is the answer.

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