Question

Explain the difference between a combination and a permutation.

Answer 1

\[k!~\binom{n}{k}=(n)_k\]

Answer 2

Sure!

Lets say you are choosing different combinations for a computer password. Then if you (for the sake of the understanding, lets say) got 12345 and you choose 5 4 different numbers, then saying

1,2,3,4 is not the same as saying 1,2,4,3 this is permutations.

Now, combinations.

You have 15 players, and choosing 5 for a team.
If you say
name1, name2, name3, name4, name5 that would be the same as saying
name1, name4, name2, name3, name5

because the same ppl are playing.

Answer 3

one is a multiple of the other

Answer 4

a permutation depends on order, it counts the number of shuffles a set of elements can take

a combination does not consider order and simply counts the number of groupings that a set of elements can take

{a,b,c} has 6 permuations:

abc
acb
bac
bca
cab
cba

but it only has one combination:

abc: in any order.

Answer 5

simply:
permutation is generally done when you need to find the number of ways a "set of things can be arranged " and combination is when you need to find the no of ways "a set of things can be selected".

Answer 6

nPr is r! times greater than nCr

Answer 7

if you try to calculate each in terms of n and r

\(\LARGE\color{black}{ \bf nCr=\frac{n!}{r!(n-r)!}}\)

\(\LARGE\color{black}{ \bf nPr=\frac{n!}{(n-r)!}}\)

Answer 8

\[k!~nCk=nPk\]
\[nCk=\frac{nPk}{k!}\]

Answer 9

yeah ... had trouble reading that sentence lol