![]() ![]() Let's take a second and figure out what 24 actually represents, 24 is the number of ways you can arrange "pencil" with "pen" being a single letter, but we got 6 of those (pen, nep, epn. And "pencil" just became a 4 letters word, so it has 4! ways of being arranged, therefore 24 ways. Now we're doing it with 3 letters "p e and n" so there are 3! ways of arranging them, therefore 6 ways. Finally we added them together to get our answer. But really we looked at all the different ways to arrange 2 items, and there was 2! ways of doing it, so 2 ways and "pencil" was treated as a 5 letters word. With "e" and "n" we figured out that "en" and "ne" were the only two possible way to arrange them, and treated them as a single letter. ![]() Now to dig in a little deeper what if we wanted "p e and n" to always be together ? Have a go at it before looking below :) ![]() There we go ! There are 240 different ways to arrange "pencil" so that e and n are always next to each other. First let's think about it a bit, to figure out how many ways you can arrange "Pencil" with N and E always next to one another it's going to be all the different ways to arrange "pencil" as if "en" was a single letter and the same thing with "ne"ġ) How many ways can we arrange Pencil as if "en" was a single letter?ĥ! = 120 ways, we have 5 things to arrange P c i l and "en"Ģ) Now how many ways can we arrange Pencil as if "ne" was a single letter? ![]()
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