<p>I know how to use them but not when, like when to use nCr and not nPr or counting and not nCr/permutations</p>
<p>Plug and chug. Got me many 800s in math.</p>
<p>nPr = n(n-1)…(n-r+1) counts the number of ways to choose r objects from a set of n (different) objects, where order <em>does</em> matter. This is easily seen from the formula since there are n ways to pick the first element, n-1 ways to pick the second element, …, n-r+1 ways to pick the rth element.</p>
<p>nCr = (nPr)/r! = n(n-1)…(n-r+1)/r! = n!/((n-r)!r!) counts the number of ways to choose r objects from a set of n where order <em>does not</em> matter.</p>