How many 3 different digit integer can be formed using 6

Question

How many 3 different digit integer can be formed using 6 no's 1,2,3,4,5, 6, if no digit is to be repeated?

Is this permutation or a combination problem? I mean is it 6c3 or 6p3?

apache · Answer

auniyal,
let me first explain you the basic diffrence between permutaion and combination.
permutaion is applied when we have to arrange things.
and combination is used when we have to select things.
let take an example SET s = {a,b,c,d}
now we have to make a word with two letters.
then its 4P2.
and if we have to select 2 letters
then its 4C2.

if we go fundamentally the difference is that in combination order is not important ie ab is same as ba.

whereas in permutation ab and ba are diffrent.

now you tell what should be used in the que you posted. :-D

Himalayan · Answer

= 6x6x6 - 6x5 - 6
= 6 x 31 = 180

Bluebird · Answer

Using the explanation given by apache above, wouldn't it be a permutation? So, the equation would be 6!/(6-3)! = 6!/3! = 120

This is different than what Himalyan got...do I have the right idea or am I missing something?

Thanks!

Sergey_is_cool · Answer

I'm getting 6!/(6-3)!=6*5*4=120 

how do you get your answer?

Himalayan · Answer

agreed. its 6x5x4 = 120

i did the other way counting all same digits and 2 same digits but missed something.

perfect.

auniyal · Answer

correct me if i am wrong, 
okay, out of 6 digits , 3 digits are selected
So, its permutation:- as order is not important, so 6p3 = 6*5*4 = 120

but how did u make sure that digits are not repeated, coz 123 is okay but 112 is not? how was numbers like 112 or 121 truncated from the result.

apache · Answer

auniyal,
 first of all order is important as 123 and 324 are two diffrent digits.

now for your question that  how did u make sure that digits are not repeated 

How many 3 different digit integer can be formed using 6 no's 1,2,3,4,5, 6, if no digit is to be repeated? 

when digits are not repeated =6*5*4 = 6P3
when digits are repeated = 6*6*6

so premutaions are only used when it is assumed that once object is taken it will not be repeated .

How many 3 different digit integer can be formed using 6

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