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<p>Number 14</p>
<p>I see how to do it, but I tried doing 5c1, since I thought it was a combination problem...
Seeing as how it said, how many different painted designs are possible, meaning order didn't matter..</p>
<p>didn't think the solution would be that simple, considering it was number 14/16.</p>
<p>Assuming we are looking at circle (as opposed to a baseball), the order of color 1 and color 2 does matter.</p>
<p>So permutations of 5 items taken 2 at a time = 5 x 4 or 5!/(5-2)!</p>
<p>If the order did not matter, then 5C2 ( =10) would be correct.</p>
<p>whats the answer? i got 10.</p>
<p>You guys did exactly what I did. Woops did a typo I mean 5C2.
I got 10 as well. The answer is actually 5x4=20, surprisingly.</p>
<p>When I looked at the question, order matters, definitely. There isn't even the question of symmetry.</p>
<p>^How did you tell? Doesn't it say "differently painted designs?"?</p>
<p>
white center + black sides
is different from
black center + white sides.
Order does matter.</p>
<p>
</a></p>
<p>Are these different?</p>
<p>Oh I see now. Thanks!</p>
<p>i still dont underatsnd this one. Can anyone help please></p>
<p>Yeah, could someone clarify the solution to this problem?</p>
<p>Basically you have five colours. You have to colour in the shape as shown below, which is Colour 1 - Colour 2 - Colour 1, which just means that there are two different places to put the colours. </p>
<p>Analogy: You have 5 bracelets. You want to wear one bracelet on the left, and one bracelet on the right. How many ways are there of wearing them?</p>
<p>Listing Method<br>
Left/Right Center
1 Colour 1 Colour 2
2 Colour 1 Colour 3
3 Colour 1 Colour 4
4 Colour 1 Colour 5
5 Colour 2 Colour 1
6 Colour 2 Colour 3
7 Colour 2 Colour 4
8 Colour 2 Colour 5
9 Colour 3 Colour 1
10 Colour 3 Colour 2
11 Colour 3 Colour 4
12 Colour 3 Colour 5
13 Colour 4 Colour 1
14 Colour 4 Colour 2
15 Colour 4 Colour 3
16 Colour 4 Colour 5
17 Colour 5 Colour 1
18 Colour 5 Colour 2
19 Colour 5 Colour 3
20 Colour 5 Colour 4</p>
<p>Permutation method</p>
<p>nPr is the number of permutation (ordered pairs) that you can have, given n options and r number necessary.</p>
<p>E.g. I want to choose two people to act as Romeo and Juliet. I have 10 cast members. How many different pairs of Romeo and Juliet can I have?</p>
<p>Answer: 10 P 2 (10 options, 2 needed)</p>
<p>E.g. I miss my 7 friends. I will go out with all 7 of them this week, one each day from Monday to Friday. How many different social calendars can I have?</p>
<p>Answer: 7 P 7 (7 options, 7 needed)</p>
<p>Solution to this example:</p>
<p>Since we have 5 options of colours, and 2 needed to colour it in, how many different shapes?</p>
<p>Answer: 5 P 2 (5 options, 2 needed)</p>
<p>Thanks for the very nice explanation fiona. Thank you. How do you know to use permutation for this one and not combination?</p>
<p>Combination is non-ordered pairs.</p>
<p>E.g. I want to choose two people to wash my toilet. I have 10 slaves. How many different pairs of toilet-washers can I have?
10C2. Because it doesn't matter, I just want them to wash my toilet :D It doesn't matter the order.</p>
<p>E.g. I want to choose two actors to be Romeo and Juliet. I have 10 cast members. How many different pairs of Romeo and Juliet can I have?
10P2 because it matters who's Romeo and who's Juliet.</p>
<p>E.g. I love cocktails. One day, I decided to mix two alcoholic drinks to get a new drink. I have 5 different types of liquor. How many different new drinks can I get?
5C2 because non-ordered pairs. Whether you mix beer and whisky or whiskey and beer it is the same.</p>
<p>E.g. I have 7 bracelets. I decided to wear one on my wrist and one on my ankle? How many different get-ups do I have?
7P2 because wearing the pearl bracelet on the wrist and bead bracelet on ankle is different from wearing bead bracelet on wrist and pearl bracelet on ankle.</p>
<p>lmao great examples. slaves to wash toilets? very nice. lol</p>
<p>And thanks so much for these examples. You cleared up a lot for me. So combination doesnt matter at all which ones or order is used but perm does. first number is total number, and second is numebr you need.</p>
<p>So for the original problem, what gives away which of these two you need to use?</p>
<p>yep, its a permutation because the colors can be switched from inside to outside and it would be different</p>
<p>5P2=20</p>
<p>Just use 5P2</p>
<p>Cuz when you see the pattern, it will be different for which order you have, say black-white or white-black. (see the picture that I linked to)</p>
