find the soln
Find the number of integral solution to |A| + |B| + |C| = 15.
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If we take one of the number as 0 then the rest two can be selected in 15
different ways. (0+ 15, 1 + 14 , 2 + 13, . . .15 + 0)
If we take one of the number as 1 then the rest two can be selected in 14 different ways. (0+ 14, 1 + 13 , 2 + 12, . . .14 + 0)
. . . .
. .
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Total number of ways = 15 + 14 + . . . . . + 1 = 15 x 8 = 120
Number of ways selecting one number out of the three |A| , |B| and |C| = 3
So Max possible solutions are 3 x120 = 360
if a,b,c are considered to be different the number of +ve integral solutions is
17!/(15!*2!) = 136.
now each of the variables can be +ve or negative thus total solutions =
136 * 2 *2*2 = 1088.
if the a,b,c are indifferent the number of 3 partitions of 15 is the nearest integer to (15^2/12)*2*2*2 = 152
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