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# how do you distinguish between permutation and combination

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how do you distinguish between permutation and combination

Guest May 7, 2015

#2
+78557
+10

Let me add one thing to what Melody said.....

Combinations count sets

Permutations count orderings within the sets

Thus, with sets of more than one element.....the number of permutations will be larger than the number of combinations....!!!

CPhill  May 7, 2015
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#1
+90970
+10

Good question!

Say you have 3 objects  A,B, and C

All the combinations of 2  are   AB,AC, and BC  there are no others   There are 3 combinations of 2 objects

The order that the objects are selected in is NOT important.

BUT

All the permutations of 2 are     AB, BA, AC, CA, BC, and CB    There are 6  pemutations of 2 objects

You see, with permutations the order is important!

Melody  May 7, 2015
#2
+78557
+10

Let me add one thing to what Melody said.....

Combinations count sets

Permutations count orderings within the sets

Thus, with sets of more than one element.....the number of permutations will be larger than the number of combinations....!!!

CPhill  May 7, 2015
#3
+90970
+5

So if you have the alphabet with 26 letters.

the number of combinations of 26 is just 1

BUT

the number of permutations is        \$\${\mathtt{26}}{!} = {\mathtt{403\,291\,461\,126\,605\,635\,584\,000\,000}}\$\$

so there are a 'few' more permutations than combinations   LOL

Melody  May 7, 2015

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