Aptitude - Permutation and Combination - Discussion

In how many different way can the letters of the word CREAM arranged.

Actually 6 letter so we got 6*5*4*3*2*1= 720 but e 2 time repeated so we divided 720/2=360.

I have a similar doubt,

I have 2 each of 24 different colors, how many 12 color combinations are possible?

First the word letter it can come in 5 different ways and the word letter have 6 words.

Please explain following question I am not understand what is mean by 6! = 360?
(1!) (2!) (1!) (1!) (1!).

!- what is this?

It is a permutation question, in which some letters are repeated so it can be solved as, ans = 6!/2! =720/2 = 360.

Yes friends answer 360 is correct because E is repeated 2 times.

Lets look at it this way:

In LEADER, there are 2 Es and 4 Unique alphabets (LADR).

Now selection of 2 Es in any of the 6 positions is a combination problem. Hence E can be selected in 6C2 ways. Which is 6x5/2! = 15.

For each of these 15 choices of E, there are 4 remaining slots for 4 unique alphabets. Hence this is a permutation problem. The 4 unique alphabets can be arranged in 4! ways i.e. 4 x 3 x 2 x 1= 24.

Therefore total ways of arranging is 15x24 = 360.

It is asking how many way not how many different ways.

So, answer should be 6! = 720.

Can anybody explain me when permutation & when combination used?