SOLUTION: please help How many arrangements of the letters in the word OLIVE can you make if each arrangement must use three letters? please explain the answer A)20 b)60 c)8*7*6*5*4*3*

SOLUTION: please help How many arrangements of the letters in the word OLIVE can you make if each arrangement must use three letters? please explain the answer A)20 b)60 c)876543

Question 40624: please help
How many arrangements of the letters in the word OLIVE can you make if each arrangement must use three letters?
please explain the answer
A)20
b)60
c)8*7*6*5*4*3*2*1
Found 2 solutions by kev82, josmiceli:
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,
I don't quite understand the question. So I'm going to restate it as what I think it means, and hopefully we'll both be on the same wavelength. Using any of the letters O, L, I, V, E at most once. How many distinct three letter words can you make?
This is quite simple really. You just have to think about how many choices there are for each letter of your three letter word.
For the first letter you can choose any one of the five letters.
For the second letter you can only choose four letters as you've already taken one of them.
For the third letter you can choose any of the three remaining letters so in total that is 5*4*3=60 different words.
I don't know whether you've met it yet, but there is a function callled the permutation function that works this out.

So P(5,3)=120/2=60.
Hope that helps,
Kev
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Lay out all possible 1st letters in the 3-letter word
O
L
I
V
E
What are the choices for the 2nd letter in each case?
O and any one of the remaining 4 letters L,I,V,or E
L and any one of the remaining 4 letters O,I,V,or E
I and any one of the remaining 4 letters O,L,V,or E
V and any one of the remaining 4 letters O,L,I,or E
E and any one of the remaining 4 letters O,L,I,or V
So, for each of 5 possible 1st letters, ther are 4 possible
2nd letters. That makes 5 x 4 = 20 possibilities so far
Now include the possibilities for the 3rd letter
O AND any one of the remaining 4 letters L,I,V,or E AND one of 3 letters left
L AND any one of the remaining 4 letters O,I,V,or E AND one of 3 letters left
I AND any one of the remaining 4 letters O,L,V,or E AND one of 3 letters left
V AND any one of the remaining 4 letters O,L,I,or E AND one of 3 letters left
E AND any one of the remaining 4 letters O,L,I,or V AND one of 3 letters left
For each of the 4 2nd letters on each line, there are 3 possible
3rd letters
O AND 4 X 3 possible 2nd and 3rd letters
L AND 4 x 3 possible 2nd and 3rd letters
I AND 4 X 3 possible 2nd and 3rd letters
V AND 4 x 3 possible 2nd and 3rd letters
E AND 4 x 3 possible 2nd and 3rd letters
The toal is 5 x 4 x 3 = 60 possible 3 letter words from olive
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