<p>A craftsperson has sic different kinds of seashells. How many different bracelets can be constructed if only four shells are to be used in any one bracelet?
a) 90
b) 45
c) 60
d) 360
e) 180</p>
<p>Answer is 45. I know I have to use combinations but i didnt get 45.</p>
<p>good question…alright well this is how you solve it…</p>
<p>I’m too lazy to explain (if someone else wants to they can)</p>
<p>6 nCr 4) + (6!/4!) = 45</p>
<p>maybe there’s a better way, who knows…but that’s the way I would do it</p>
<p>y do u add 6!/4!?</p>
<p>Je ne comprends pas!</p>
<p>If there are six seashells then the total amount of combinations would be 6!</p>
<p>Since you can only have 4 seashells in a bracelet though you would have to take (6x5x4x3)/(4x3x2x1) = 15</p>
<p>Someone explain to me why that isnt right</p>
<p>answer
now</p>
<p>we have to do nCr(6,4) to find how many random combinations of 4 differetn bracelets we can get. THis is 30. The total number of possible combinations in this scenario is not 6!.</p>
<p>then you just add it up.</p>
<p>here’s another way of doing it</p>
<p>draw a picture of the bracelet, with four dots representing the shells. In the first dot, you have 6 choices of shells, in the next you have 5 choices, the next you have 4 choices, and the next you have 3. so thats 6x5x4x3 combinations, which is 360. But then, you have to divide it by 4. Why? Because you can rotate the shells around 4 times and still have the same bracelet. So then you have 90. Finally, you have to divide 90 by 2. This is because you can flip the bracelet over and it will still be the same. So your answer is 45.</p>
<p>Why is the answer 45 and not 15?</p>
<p>(6x5x4x3)/(4!) = 15</p>
<p>Also why divide by 4? It should be divide by 4!</p>
<p>you divide by 4 because the shells could be rotated 4 times around the bracelet into different positions. for example, shell 1 would go to shell2’s place, and so on. shell 1 could then move to shell3’s place, and so on. this could happen a total of 4 times. the order remains the same, just the place on the bracelet has moved. so you divide by 4 (and then by 2 for the reason i listed above)</p>
<p>however, if this question were about ppl at a table, you wouldn’t divide by 2 cause u cant flip a table around/upside down/whatever like you can w/ a bracelet</p>
<p>alright well you can also do it sauvage’s way…and in math terms its simply</p>
<p>nPr(6,4) / (2*4)</p>
<p>that gives you 45…I guess mine was complicated</p>
<p>Oh ok, I get it. I think this is a unique case because the bracelet is circular? I imagined the bracelet to be straight.</p>
<p>merudh, how did you arrive at 6c4 + 6!/4! ?</p>
<p>lol its simple nCr(6,4) + nPr(6,2) = 45</p>
<p>try it.</p>
<p>yeah its a circular permutation</p>
<p>merudh, i still don’t understand-- why is the equation nCr (6,4) + nPr (6,2)? i see that it works…but why???</p>