Roll a dice 4 times

X =smallest faceobserved

Given P(X=6) = 1/1296

Find:

P(X=1)

P(X=2)

P(X=3)

P(X=4)

P(X=5)

I got 216/1296, 125/1296, 64/1296, 27/1296, and 8/1296 for P(X=1) through P(X=5) respectively. I think I did something wrong as the numerators don't add up to 1296 like I thought they would.

Help is appreciated.

This is a probability distribution function by the way.