Question

Explain the difference between combination and permutation in your own words. GIVE EXAMPLES PLEASE. NOT COPIED OFF GOOGLE FROM YOU.. :))

Answer 1

Take three numbers: 1, 2, and 3.

Write all the possible arrangements of two of these numbers:
12
13
21
23
31
32
(six total)

In terms of the permutation formula, you are counting the number of DISTINCTLY ORDERED strings of numbers. By this, I mean strings that use the same numbers like 12 and 21 are different from one another. In the list are all the possible permutation of two of the three numbers.

The combination formula lets you count all the strings of numbers that CONTAIN DISTINCT ELEMENTS. In other words, 12 and 21 are the same because they're made of the same two numbers, but 12 and 13 are not. From the list above, these would be
12 (because 21 is the same)
13 (because 31 is the same)
23 (because 32 is the same)
which brings you a total of 3.

So from three numbers, we pick out 2. You have the following counts:
\[\large{}_{3}P_{2}=\frac{3!}{(3-2)!}=6\\
\large{}_{3}C_{2}=\frac{3!}{2!(3-2)!}=3\]