<p>Hello all,
I need a little bit of help with a math problem in the old BB. The problem reads as follows:</p>
<p>"Exactly 4 actors try out for the 4 parts of a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible?"</p>
<p>I know what the answer is (24) but I know there is some formula to obtain this value and if anyone could show me that formula or any other way to this problem I would really appreciate it.</p>
<p>Thanks!</p>
<p>This is an example of a permutation, which gives you ordering. The formula for a permutation is n!/(n-r)!, where n is the number of objects and r is the number of “slots” or positions. Plugging in you get 4!/(4-4)! = 4! = 4<em>3</em>2*1 = 24.</p>
<p>^A different (but fundamentally similar) approach is to draw four blank spaces on a sheet. Each blank space represents a role. For the first role you have four options (all four people). For the second role you have three (the four people minus the person selected for the first role). For the third you have two. And for the fourth you have one. So, it looks like 4, 3, 2, 1, all of which you multiply together to get 24.</p>
<p>Thanks so much. I always forget those factorial formulas haha.</p>