<p>Exactly 4 actors try out for the 4 parts in 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>4 Parts in the play: 1,2,3,4
4 Actors possible: A,B,C,D</p>
<p>Any of the 4 actors could take part 1. Then any of the three remaining could take part 2. Then either of the two remaining could take part 2, then the last person takes part 4. </p>
<p>4P4 = 4x3x2x1 = 24 different assignments</p>
<p>Thanks Chrisiskey.</p>
<p>Where'd you get 4P4.. and what does it mean?</p>
<p>4P4 = 4 permute 4 = how many ways can you arrange 4 objects in a group of 4 things? This comes from probability. Look up permutation and combination functions.</p>
<p>Ok. Thanks. I haven't taken Probability.</p>
<p>luckily you can use common sense in this case.</p>
<p>May I ask you a question?</p>
<p>Say it was:</p>
<p>4 Parts in the play
5 Actors possible</p>
<p>How would you go about solving that?</p>
<p>You would use the same logic chrisiskey used. For the first part, there are 5 possibilities; 5 available actors. For the second part, since one is used up for the first one, there are only 4 left. For the third there are only 3, and for the fourth there are only 2. Therefore:</p>
<p>(5)(4)(3)(2) = 120 different assignments</p>
<p>Thanks, jaime. That's what I thought, but I wasn't completely sure.</p>
<p>Wait a second, Jaime, based on your logic.. And the question I stated:</p>
<p>"Say it was:</p>
<p>4 Parts in the play
5 Actors possible"</p>
<p>Shouldn't it be...</p>
<p>5(3)(2)= 30.. since there are only 4 parts..??</p>
<p>I am afraid I don't see how it could be so, Big Dreams. There are only four parts, and by the given statements of the problem, each actor can perform any part and no actor performs more than one part. Therefore, assuming each actor plays a part, we must input in the number of potential actors for each of the available parts.</p>
<p>Let us simplify this into an easier problem. Suppose three actors, Abolsky, Zelenty, and Marino, want to participate in a 2 part play directed by Olwell. Each one can play any one part, and no actor will perform more than one part. Therefore, first let us solve with my logic.</p>
<p>(3)(2) = 6</p>
<p>And now let us check by taunting. In the following list, the first person plays the first part, while the second plays the second.</p>
<p>Abolsky Zelenty
Abolsky Marino
Zelenty Abolsky
Zelenty Marnio
Marino Abolsky
Marino Zelenty</p>
<p>Thus giving us 6 possible combinations, which checks with my answer. If you care to write the 120 possible combinations for the above problem, you should see that, it too, checks.</p>
<p>Of course, in all of these cases we are assuming that all the parts will be filled by actors. I am wondering whether that is a reasonable assumption; I do not think any information given implies this to be the case. Should it be so, for any part, there would be n+1 possibilities, where n is the number of actors and 1 represents the possibility that none of the actors will play that part. What do you people think?</p>
<p>Oh ok. Thanks. I see I didn't read my own questions. ;) Thanks a lot.</p>