Ev-En-Ly Distributed
Probability
Level
pending
In how many ways can you distribute 54 among Ev, En and Ly in such a way that Ly always gets an even number? Note: Everyone gets something.
The answer is 676.
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1 solution
The question is equivalent to finding non-zero solutions for natural numbers x, y and z such that x + y + 2z = 54. When z = 26, x + y = 2 and there is only 1 way that being (1, 1). When z = 25, x + y = 4 giving 3 solutions (1, 3) , (2, 2), (3, 1). In general for x + y = p there are (p - 1) ways. For z taking values from 26 down to 1, 1 + 3 + 5 + . . . . . . + 5 1 = 2 6 2 = 6 7 6