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6 is not a mixed number so there cannot be three correct ways to show it as one.
2/3 4/6
Assuming the dice are unbiased standard dice, then To get a mean average of 6, every dice must show a six → probability = 1/(6^4) = 1/1296 ≈ 0.000772 To get a median average of 6, then only 3 of the dice need show a six. In this case there are: all 4 dice show a 6 = 1 way To select 3 dice to show 6 leaves 1 die which can show any number 1-5. There are 4 ways this single die can be left giving 5 × 4 possible ways = 20 ways This gives a total of 1 + 20 = 21 ways of it happening and the probability is 21/1296 ≈ 0.0162 To get a mode average of 6 is slightly complicated: all 4 dice can show a 6, three dice can show a 6 ,or 2 dice can show a 6 AND the other 2 dice show different numbers. There are: 1 way all 4 show a 6 (as above) 20 ways exactly 3 show a 6 (as above) 2 show a six: 2 dice are selectable in 4 × 3 = 12 ways. Of the other 2 dice one can show one of 5 numbers and the other one of the remaining 4 which is 5*4 = 20, making 12*20 = 240 ways Thus there are a total of 240+20+1 = 261 ways of it happening and the probability is 261/1296 ≈ 0.2014
There are 3 ways an even number can show up on the first die. AND There are 3 ways an even number can show up on the second die. AND There are 3 ways an even number can show up on the third die. So since "AND" means "MULTIPLY", there are 3x3x3 or 27 ways the three dice can all come up even. So the numerator of the probability is 27. We calculate the denominator of the desired probability: There are 6 ways any number can show up on the first die AND There are 6 ways any number can show up on the second die AND There are 6 ways any number can show up on the third die So since "AND" means "MULTIPLY", there are 6x6x6 or 216 ways the three dice can all come up any number. So the denominator of the probability is 216.
6 ways.6 ways.6 ways.6 ways.