How many different arrangements can be made with the letters of the word algebra? in how many ways of these arrangements will l and r be next to each other? How will I do this?
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What have you tried? Have you seen any similar problems before? – Integrand Sep 15 '20 at 17:15

Rule of product. (*For second part, pick whether $L$ is to the left or the right of $R$*) Pick the position that the $L$ is in. Pick the position that the $R$ is in. Pick the positions that the A's are in. Pick the position that the G is in. Pick the position that the E is in. Pick the position that the B is in. Apply rule of product and conclude. – JMoravitz Sep 15 '20 at 17:16
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Consider to read this post.
For the first question consider that to arrange $7$ different items you have $7!$ permutations. But you have two $a$ , so you can interchange them which means you can divide the total number by $2!$ then the result is $\frac{7!}{2!}$.
Now for the second one consider that you can put $lr$ or $rl$ in any of the possible six positions available ( remember that you have $2$ letters to place), and then you rearrange all the other letters as usual. So the result is $2 \cdot 6 \cdot \frac{5!}{2!}$.
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