Combinatorics

Choose and arrange

Combinations and arrangements, with or without repeats.

For checking your work after you’ve tried it yourself.

Step 1:
Type n and k

n things, pick k of them.

Step 2:
Answer two questions

Does order matter? Can things repeat?

Step 3:
Read the count

And see every choice when there are only a few.
What it does.
Counts the ways to pick kk things from nn. Two questions decide the formula: does the order matter, and can the same thing be picked twice? It shows all four counts and highlights yours.
When it helps.
Checking a count you worked out, and seeing which formula fits.
What it won’t do.
It counts; it doesn't decide which question your problem is asking.
Example.
Choosing 3 of 5 when order doesn't matter: (53)=10\binom{5}{3} = 10.
Does order matter?
Can things repeat?
Pick kk things from nn

n and k from 0 to 10000.

Try