Example: Ways to arrange colors

Permutations and combinations

Permutations
Combinations
Counting 2
Example: Ways to arrange colors
Example: 9 card hands
Example: Ways to pick officers
Permutations
Combinations
Permutations and combinations

Example: Ways to arrange colors Thinking about how many ways you can pick four colors from a group of 6

Back

Example: Ways to arrange colors

⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.

In one game, a code made using different colors is created by
one player, the codemaker, and the other player, the
codebreaker, tries to guess the code.
The codemaker gives hints about whether the colors are
correct and in the right position.
All right.
The possible colors are blue-- let me underline these in the
actual colors-- blue, yellow, white, red, orange and green.
Green is already written in green, but I'll underline it
in green again.
And green.
How many 4-color codes can be made if the
colors cannot be repeated?
To some degree, this whole paragraph in the beginning
doesn't even matter.
If we're just choosing from-- let's see, we're choosing
from-- how many colors are there?
There's 1, 2, 3, 4, 5, 6 colors, and we're going to
pick 4 of them.
How many 4-color codes can be made if the
colors cannot be repeated?
And since these are codes, we're going to assume that
blue, red, yellow and green, that this-- that that is
different than green, red, yellow and blue.
We're going to assume that these are not the same code.
Even though we've picked the same 4 colors, we're going to
assume that these are 2 different codes, and that
makes sense because we're dealing with codes.
So these are different codes.
So this would count as 2 different codes right here,
even though we've picked the same actual colors.
The same 4 colors, we've picked them
in different orders.
Now, with that out of the way, let's think about how many
different ways we can pick 4 colors.
So let's say we have 4 slots here.
1 slot, 2 slot, 3 slot and 4 slots.
And at first, we care only about, how many ways can we
pick a color for that slot right there, that first slot?
We haven't picked any colors yet.
Well, we have 6 possible colors, 1, 2, 3, 4, 5, 6.
So there's going to be 6 different possibilities for
this slot right there.
So let's put a 6 right there.
Now, they told us that the colors cannot be repeated, so
whatever color is in this slot, we're going to take it
out of the possible colors.
So now that we've taken that color out, how many
possibilities are when we go to this slot, when we go to
the next slot?
How many possibilities when we go to the
next slot right here?
Well, we took 1 of the 6 out for the first slot, so there's
only 5 possibilities here.
And by the same logic when we go to the third slot, we've
used up 2 of the slots-- 2 of the colors already, so there
would only 4 possible colors left.
And then for the last slot, we would've used up 3 of the
colors, so there's only 3 possibilities left.
So if we think about all of the possibilities, all of the
permutations-- and permutations are when you
think about all the possibilities and you do care
about order; where you say that this is different than
this-- this is a different permutation than this.
So all of the different permutations here, when you
pick 4 colors out of a possible of 6 colors, it's
going to be 6 possibilities for the first 1, times 5 for
the second bucket, times 4 for the third or the third bucket
of the third position, times 3.
So 6 times 5 is 30, times 4 is times 3.
So 30 times 12.
So this is 30 times 12, which is equal to their 360 possible
4-color codes.

Questions
Tips & Feedback

Be specific, and indicate a time in the video:

At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content?

Post a tip or feedback
General discussion about the site
Report a technical problem with the site
Request a video or feature

This discussion area is not meant for answering homework questions.

Formatting tips

Cancel or

( total)

Share a tip

When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

Suggest a fix

At 2:33, Sal says "double bonds" but should say "single bonds."

Have something that's not a tip or feedback about this content?

Ask a question
General discussion about the site
Report a technical problem with the site
Request a video or feature

This discussion area is not meant for answering homework questions.

Formatting tips

Cancel or

Discuss the site

For general discussions about Khan Academy, visit our Reddit discussion page.

Flag inappropriate posts

Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.

abuse

disrespectful or offensive
an advertisement

not helpful

low quality
not about the video topic
soliciting votes or seeking badges
a homework question
a duplicate answer
repeatedly making the same post

wrong category

a tip or feedback in Questions
a question in Tips & Feedback
an answer that should be its own question

about the site

a question about Khan Academy
(Visit our FAQ)
a post about badges
a technical problem with the site
(Report a problem)
a request for videos or features