Ev-En-Ly Odd
Probability
Level
3
In how many ways you can distribute 55 among Ev, En and Ly so that everyone gets (a positive) odd number? (In other words three odd numbers add up to 55).
The answer is 378.
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Suppose you have 55 marbles to be distributed among 3 people. Set aside 3 lone ones (1 lone marble for each person) and group the remaining 52 into 26 pairs. Now imagine distributing 26 pairs of marbles into 3 boxes, there are ( 2 6 + 3 − 1 ) C ( 3 − 1 ) = 2 8 C 2 = 3 7 8 ways.