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

Algebra ->  Permutations -> 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      Log On


   

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) About Me  (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:



n%21%2F%28n-r%29%21 Start with the given formula



5%21%2F%285-2%29%21 Plug in n=5 (this is the total number of letters that you have) and r=2 (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.



5%21%2F3%21 Subtract 5-2 to get 3



Expand 5!
%285%2A4%2A3%2A2%2A1%29%2F3%21



Expand 3!
%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%29



%285%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%29 Cancel



5%2A4 Simplify




20 Now multiply 5*4 to get 20


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



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