SOLUTION: How many two-letter permutations can be made from the letters L,M,N,O, and P? How many three-letter combinations can be made from the letters in the word BLACK? Than

Question 117767: How many two-letter permutations can be made from the letters L,M,N,O, and P?
How many three-letter combinations can be made from the letters in the word BLACK?

Thanks whoever helps me because I am totally confused.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to show you 2 ways you can tackle these types of problems

Method #1:

Since 2 only places to put them, you can visualize of the problem as a series of slots like this:

_ _

Now since you have 5 distinct letters, you have 5 choices for the first slot. Once you take away one letter, you are left with 4 letters. So you'll have 4 choices for the 2nd slot. Now simply multiply these two numbers to get

5*4=20

So you'll have 20 unique combinations

Method #2:

Since we're talking about permutations, we can use the permutations formula:

Start with the given formula

Plug in (this is the total number of letters that you have) and (this is the number of letters that you can use at one time) note: the value of n is greater than r. In other words n>r.

Subtract to get 3

Expand 5!

Expand 3!

Cancel

Simplify

Now multiply 5*4 to get 20

So 5 choose 2 (where order does matter) yields 20 unique combinations

---------

So no matter what method you choose, you'll get the same answer.
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