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Ronch [10]
3 years ago
6

How many ways are there to arrange the letters a, b, c, and d such that a is not followed immediately by b?

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
4 0
First, let's determine how many combinations there are without any restrictions. There are 4 letters, so we have 4 options to choose from for the first letter. For the second letter, there are only 3 options, for the third there are only 2 options, and finally for the last letter there is just 1 option. Therefore, we have:

4! = 4 \times 3 \times 2 \times 1 = 24 options

Now we can subtract the number of combinations in which a is immediately followed by b.

Instead of having 4 options to choose from, we now only have 3:

ab, c, or d

So using the same logic as before, we have:

3! = 3 \times 2 \times 1 = 6 options

Now just subtract the 6 combinations that don't work from the total:

24 - 6 = 18

The answer is 18.


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<em><u>To </u></em><em><u>find:</u></em>

<em><u>=</u></em><em><u>></u></em><em><u> </u></em><em><u>The</u></em><em><u> </u></em><em><u>value</u></em><em><u> of</u></em><em><u> </u></em><em><u>x</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x - 8 =  - 11</u></em>

<em><u>Now,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>move </u></em><em><u>-</u></em><em><u>8</u></em><em><u> </u></em><em><u>to </u></em><em><u>the</u></em><em><u> </u></em><em><u>other</u></em><em><u> </u></em><em><u>side </u></em><em><u>i.e </u></em><em><u>the </u></em><em><u>RHS </u></em><em><u>side,</u></em>

<em><u>which</u></em><em><u> </u></em><em><u>results</u></em><em><u> </u></em><em><u>in </u></em><em><u>the </u></em><em><u>change</u></em><em><u> </u></em><em><u>of </u></em><em><u>it's</u></em><em><u> </u></em><em><u>sign(</u></em><em><u>-</u></em><em><u> </u></em><em><u>converts</u></em><em><u> </u></em><em><u>into </u></em><em><u>+</u></em><em><u>)</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x =  - 11 + 8</u></em>

<em><u>Now </u></em><em><u>,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>add </u></em><em><u>the </u></em><em><u>Numbers</u></em>

<em><u>=</u></em><em><u>></u></em>

<em><u>x =   - 3</u></em>

<h2><em><u>Hence</u></em><em><u>,</u></em><em><u>-</u></em><em><u>3</u></em><em><u> </u></em><em><u>is </u></em><em><u>the</u></em><em><u> </u></em><em><u>required</u></em><em><u> </u></em><em><u>answer</u></em><em><u>.</u></em></h2>

<em><u>^</u></em><em><u>-</u></em><em><u>^</u></em>

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