Permutations

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ConfusedWithMaths

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Feb 10, 2021
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Hello, I would like help with a question on permutations please.

Question: "In how many ways can four different consonants and four different vowels be arranged in a row if the four vowels are together?"
I've checked the answer to this question, however, I am very confused to why the answer would be 4! * 5!. There's only 8 numbers?
 
ConfusedWithMaths said:
Hello, I would like help with a question on permutations please.

Question: "In how many ways can four different consonants and four different vowels be arranged in a row if the four vowels are together?"
I've checked the answer to this question, however, I am very confused to why the answer would be 4! * 5!. There's only 8 numbers?
Click to expand...
Since you have to put 4 vowels together - stack the vowels together and put a band around the stack. Now you have 5 things to place - 1 stack and 4 consonants. There is your 'missing' five!
 
If we tape the four vowels together, then that block with the four consonants give five to be arranged.
That can be done in \(5!\) ways. But the block can be arranged in \(4!\) ways.
All total \(4!\cdot 5!\) ways.
 
pka said:
If we tape the four vowels together, then that block with the four consonants give five to be arranged.
That can be done in \(5!\) ways. But the block can be arranged in \(4!\) ways.
All total \(4!\cdot 5!\) ways.
Click to expand...

Thank you so much! I understand now. :)
 
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