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## High school statistics

### Course: High school statistics>Unit 6

Lesson 5: Permutations

# Ways to arrange colors

Thinking about how many ways you can pick four colors from a group of 6. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Wait, why does order matter in this example? I don't get why!!! •   If you consider the colors as letters, then you can easily see how the order matters. B-A-R-N is a completely different word than N-A-B-R, even though the same letters were used. So the order of the letters (colors) matters. Or think of four numbers. 1-2-3-4 is different from 3-1-4-2, although the same numbers are used.
On the other hand, think of a four-ingredient fruit salad. A salad made of apples, oranges, grapes, and bananas is exactly the same salad as one made of oranges, bananas, apples, and grapes. The order does NOT matter in the fruit salad.
• How do I judge whether this is a permutation question or combination question •   Permutation= Order does matter. Combination= Order does NOT matter.
• What if the colours CAN repeat? How would the process/equation change? •   6 x 6 x 6 x 6
Think about it like this: Since the colours can repeat and there are 6 alternatives, there will be 6 possible colours for every slot.
• Am not much into binary numbers and such but am wondering... Why can we store 256 different values into 8 bits and why does 8 bit translate into a decimal value of 4 decimal spaces? I know that an 8 bit color has 256 levels of black and white. And I can get any color when I mix 3 basic colors, Red, Green and Blue and using combinatronics I get 256^3 since these 3 colors can have same value or same level of shade between black and white. But why does 8 bit translate to 256 shades? •  Lets suppose you have just 2 bits. How many numbers can you represent?

``0  0  =  00  1  =  11  0  =  21  1  =  3``

So with just 2 bits we can represent 4 numbers. Notice that 2^2 = 4
Let's add another bit, now how many numbers can we represent?
``0 0 0 = 00 0 1 = 10 1 0 = 20 1 1 = 31 0 0 = 41 0 1 = 51 1 0 = 61 1 1 = 7``

So with three bits we can represent 8 numbers, 0 to 7. Notice that 2^3 = 8.
That is the pattern. So, with 8 bits we can represent 2^8=256 different numbers or levels.
• in how many ways can the first, second, and third placers be chosen from a group of 8 contestants? • Sorry i'm replying to you 8 years later, but it's better than nothing.

If you watch the Permutation formula video, you see that if you don't have enough spots for every position, you take the places, which there are 3 in this case, and then start from 8 and count down 3, if it was 4 you would count down 4, etc. So 8,7, and 6. So you multiply 8 7 and 6. And you get 336 ways that first second and third placers be chosen from 8 people.
• can anyone tell me why the factorial of 0 is 1? • And what if BRYG is considered the same as GRYB? What numbers are input into the spaces then, for calculating the answer? • Good question! He mentions that because he considers them different, he is finding permutations (P). When you consider BRYG and GRYB the same, that is called finding the number of combinations (C). You can see that there will (almost) always be fewer combinations than permutations, since lots of permutations will only count as a single combination. If you are choosing r things out a collection of n things (in this case we are choosing 4 colors out of a total of 6 colors, so r = 4 and n = 6), then C(n, r) = P(n, r) / r!, where the "!" means "factorial" (3! = 3*2*1 = 6, 5! = 5*4*3*2*1 = 120, etc.). So in this problem, the number of combinations would equal the number of permutations divided by 4! = 4*3*2*1 = 24. So if BRYG, GRYB, RGBY, etc., were considered the same, then instead of 360, the number of possibilities would be 360/24 = 15. Not very many!
• At to , wouldn't the second slot be 2? • this is a question about homework but this is not the real question: If the numbers 1-8 are used to make 3-digit numbers and they do not reapt , how many 3-digit numbers can be made? What is the formula? I don't get this. :( • in how many ways can 30 people be divided into 15 couples 