What will be the number of permutations of n different things, taken r at a time,when p particular things is to be always included in each arrangement? I know the answer to this question but could not reach to the logic behind this.How to tackle these permutations where conditions are given?
2026-04-12 08:42:11.1775983331
permutations with a given condition!
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I'm assuming we have $r\geq p$. In that case, one just needs to choose $r-p$ other items to go with the $p$ required ones, and then permute all $r$ of those in every possible way. That gives us the formula
$\binom{n-p}{r-p}\cdot r!$