<p>A singer is selecting 4 musicians to serve as her back-up band on her latest tour. She needs 2 guitarists, one bassist, and one drummer. She's choosing from a group of 7 musicians, each of whom can play guitar, bass and drums equall ywell. How many different back-up bands can she create?</p>
<p>A 28
B 70
C 210
D 420
E 840</p>
<p>Could you explain how you get the answer?</p>
<p>7!/(3!2!) = 420</p>
<p>For the guitarist positions, she can choose out of 7 for the first spot and out of 6 for the second spot. Since they want different combinations, you have to divide that number by 2! to take into account different permutations of the same combination. Person A with Person B is the same as Person B with Person A. Then you have to multiply by 5 for the bass position and by 4 for the drums position.</p>
<p>The answer is [(7<em>6)/2]</em>5*4 = 420</p>
<p>That's what I got too!
But the book(PR) thinks that it's just a permutation problem of 7<em>6</em>5*4=840 and the fact that there are 2 guitarists doesn't matter. So the book is wrong I'm guessing?</p>
<p>If the order of the guitarists mattered, then PR would be correct, but nothing in the problem would imply that the order mattered.</p>
<p>So yes the book is wrong.</p>
<p>Alright, thanks!</p>
<p>Wow. I cant believe I dont understand this at all. Can someone help?</p>
<p>This sort of question will fortunately not appear on the SAT. If the people playing guitars were not doing the exact same thing (which is more than likely) than the answer would be E. </p>
<p>Because of that the question is too confusing/ambivalent.</p>
<p>Thats a poorly constructed problem. I don't see how its 420 if it says that each person can play every instrument equally as well, i agree with PR. Since each person can play the instruments "equally well", it doesn't matter who gets picked, its just a permutations problem. Besides, Shouldn't it be "just as well" ? its still a poorly constructed problem nonetheless.</p>
<p>^ "equally well" doesn't really matter. It only tells you that all seven of them can perform all roles. The question asks "how many different back up", so say if you have musicians A, B, C, D, E, F and G, the combination of guitarists AB or BA is considered as one thing. And of course, if like lolcats4 pointed out, the guitarists are not doing the same thing, then E would be the answer.</p>
<p>But generally when they group something together by saying "2 guitarists" they mean for them to be interchangeable.</p>
<p>^ Exactly why this is a terrible question.</p>