A die is rolled 12 times. Define the maximum of the 12 rolls to be the largest of the numbers that appear on the 12 faces. For example, the maximum of the sequence "354222143351" is 5. What is the chance that the maximum is equal to 4?

I think about two approach.

1) P(max = 4) = P(max < 5) - P(max < 4) = 4^12/6^12 - 3^12/6^12

2) At least one of the dice is 4 and all other face is smaller or equal 4. We have 12 spots for a fix face 4. For the 11 left spots, each spot can has {1,2,3,4}. So, P = (12 * 4^11)/6^12

I think 1) is correct but I don't know why 2) is not correct. Please help!