Question 477431: Dear math teacher,
I am having diffulties with the following problem:
Find the number of a) combinations and b) permutations of four letters each that can be made from the letters of the word TENNESSEE.
Here is what I did so far, but got stuck/confused:
4-letter word
_ _ _ _ T E N N E S S E E
n = 9
n (vowels) = 4 = {E, E, E, E} therefore n(vowels) = 1
n (consonants) = 5 = { T, N, N, S, S} thus n (consonants) = 3
a) # of combinations = ?
b) # of permutations = ?
(no repetition allowed of same letters for permutations)
Vowels Consonants
n 1 3
r don't know don't know how to get it
E T N S
4! times 4! = 4C4 times 4! = 576 permutations but the answer is 163 permutations.
E T N S
E T S N
E S T N
Please help me figure out what to do with this problem. I got confused because the question is asking for both combinations and permutations; I also got thrown off because there are so many repeats of the letters. Please let me see how you solve it.
Thank you very much.
Yours respectfully,
Ivanka
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Could I suggest you try your problem with a smaller
example.
Use the word noon.
It has 4!/(2!*2!)= = 24/4 = 6 arrangements
---
nn00
n00n
nn00
n0n0
0n0n
00nn
-------------
How about combinations?
You have 4 elements:
4C0 = 1
4C1 = 4
4C2 = (4*3)/(1*2) = 6
4C3 = 4C1 = 4
4C4 = 4C0 = 1
It doesn't matter that there are repeating elements.
===========================
Cheers,
Stan H.
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