0
$\begingroup$

I want to solve the following:

Calculate the number of ways of selecting five distinct integers $x_1,x_2,x_3,x_4,x_5$ where $0\leq x_1 \lt x_2 \lt x_3 \lt x_4 \lt x_5 \leq 20$

I think this may be a problem of inclusion/exclusion, but it also might be a stars and bars problem.

Which type of problem is this, and how do I get it into a form that is more standard for such a problem? Thank you for any ideas.

$\endgroup$
1
$\begingroup$

You can just pick $5$ distinct elements from $\{0,1,2,\cdots, 20\}$, they automatically put themselves in the right order.

So we have ${21 \choose 5}$ ways

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.