How many possible outcomes are there when 5 similar dices are rolled ?

Question

In this question If I consider first total no of outcomes as 6^5 , then I divided it be 6C5 *5! since there are 5 similar dices so the outcome (1 2  3 4 5 ) will be similar to (5 4 3 2 1) .

Now what's wrong with this approach ?

Comments

In ur 6C5 * 5!  firstly u r selecting 5 numbers out of {1,2,3,4,5,6}   which may result as 1,3,4,5,6 but they all are distinct. But this is not the case with dice, numerals on dice may repeat. For ex: {1,2,1,1,3} respectively on five dices..

Answer 1

$\underbrace{{}^6C_5}_{\text{5 different outcomes}} +\underbrace{ {}^6C_1 . {}^5C_3 }_{\text{only 1 outcome appearing twice}}+ \underbrace{{}^6C_2 .  {}^4C_1}_{\text{2 outcomes appearing twice}} +\underbrace{ {}^6C_1 . {}^5C_2 }_{\text{one outcome appearing thrice}}+ \underbrace{{}^6C_1 . {}^5C_1}_{\text{one outcome appearing thrice and 1 outcome appearing twice}} + \underbrace{{}^6C_1 . {}^5C_1}_{\text{one item appearing 4 times}} +\underbrace{ {}^6C_1}_{\text{one outcome appearing 5 times}}\\
= 6 +  60 +60 + 60 + 30 + 30 + 6\\
=252.$

Comments

Yes , This should be the Correct Answer.

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Sir for the case when only 1 outcome is appearing twice for it in 6C1 ways I can chose one number then in 5C2 ways I can chose its position and then in 5C3*3! ways I can arrange chose and arrange rest of the numbers, how come u did 6C1*5C3 ?

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dices are similar. So, outcome 1 2 3 4 5 is same as outcome 5 4 3 2 1- that is the order in which outcome is coming does not matter.

Answer 2

for every dice we have 6 possibility which are independent of any other dice, Hence total possible outcomes if 5 similar dices are rolled, given that each outcome for a dice is equally likely is given by : $6^5$

Comments

Plz note the term similar here ,answer is 252 .