SOLUTION: How many permutations are there in the Word TELEVISION if the consonants go together

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Question 1178649: How many permutations are there in the Word TELEVISION if the consonants
go together
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
How many permutations are there in the Word TELEVISION if the consonants
go together
(TLVSN)(EEIIO)

There are 5! ways to arrange the consonants TLVSN

Let X represent any one of the 5! arrangements of consonants.
Then for each of those 5! X's, we find the number of distinguishable
arrangements of

XEEIIO

If the 2 E's were distinguishable and the 2 I's were distinguishable, there
would be 6! arrangements.  However, since they are indistinguishable we must
divide 6! by (2!)(2!).

Answer:  5%21%2Aexpr%286%21%2F%282%212%21%29%29%22%22=%22%22120%2Aexpr%28720%2F%282%2A2%29%29%22%22=%22%2221600

Edwin

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Mathematically  (i.e.  strongly/strictly speaking),  the problem is worded  INCORRECTLY.


The correct wording is  THIS 

    How many  distinguishable arrangements  are there in the word TELEVISION if the consonants go together ?