Question

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.

Answer 1

Answer:

Option A

Step-by-step explanation:

Whenever we want to arrange a number of objects or letters or numbers n then we must check whether

i) repitition is allowed

If repitition is allowed then total number of ways = n!

ii) repitition not allowed.

In this case again we have to check whether order matters or not.

If order matters then no of ways nPn.  

Here n =5

We find that nPn = 5!

Thus both are correct.

Hence option A

Answer 2

First option is correct

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.