Question

I roll a die repeatedly. Find the chance that the first 4 rolls all show different faces, and the 5th roll shows a face that has appeared before.

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Answer 1

You have 5 rolls. You want 4 different faces showing and a roll that shows any of the 4 different faces:
r1 = 6/6
r2 = 5/6
r3 = 4/6
r4 = 3/6
r5 = 4/6
You want the prb of r1 and r2 and r3 and so on