2
$\begingroup$

How many ways are there to put a total of m tennis balls, each distinctly numbered, into n distinctly marked baskets with at most one ball in each basket?

New contributor
Afra Binth Osman is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
$\endgroup$
1
  • 4
    $\begingroup$ Could you edit into your question what you have tried so far? $\endgroup$ – Henry May 4 at 9:38
1
$\begingroup$

From the problem statement, it's clear that $n \geq m.$

Step 1: Choose $m$ baskets from $n$ of them. The number of such choices is $ \binom n m.$

Step 2: Then you have $m$ balls and $m$ baskets. Place exactly one ball into a basket. There're $m!$ such ways.

Step 3: Find the total number of permutations: It's $ \binom n m$$m!$ This number is denoted by $P(n, m).$

$\endgroup$
0
$\begingroup$

Add $n-m$ numbered tennis balls into the mix, and distribute all the balls across the $n$ baskets ($n!$ ways), and then remove the dummy balls ($(n-m)!$ ways), to give $\frac{n!}{(n-m)!}$ ways in all.

$\endgroup$

Your Answer

Afra Binth Osman is a new contributor. Be nice, and check out our Code of Conduct.

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.