Statistics question, what's the chance voters for three positions picked the same candidate 50 times in a row.?

Question

There was a recent election for President, Vice President, and Treasurer. There were two Presidents, three Vice Presidents, and two Treasurers running. Question; what is the likelihood that fifty (50) voters in a row would choose the same three candidates?

President 1 of 2

Vice President 1 of 3

Treasurer 1 of 2

50 times in a row

Answer 1

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the 1st man can choose any one from each category

P[2nd man chooses the same 3] = [1/2][1/3][1/2] = 1/12

P[3rd man chooses the same 3] = -ditto- = 1/12

. . . . . . . . . . . . . . . . . . . .

& -ditto- upto the 50th man

thus reqd. probability = [1/12]^49