You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain. Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time. Your friend is correct because applying the permutations rule in this setting would be inappropriate. Neither method is correct. The combinations rule should be applied in this setting. Your method is correct because you are applying the permutations rule in the appropriate setting.

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You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain. Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time. Your friend is correct because applying the permutations rule in this setting would be inappropriate. Neither method is correct. The combinations rule should be applied in this setting. Your method is correct because you are applying the permutations rule in the appropriate setting.

Algebra
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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It's not the last one :/
Maybe it's the first?
well, the permutation rule gives us 5!/(5-5)! = 5! so both methods are correct

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Thanks :)

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