# Math Help - permutations

1. ## permutations

hi,
i have a problem in permutations

how many word with or without meaning can be formed from the letters of the word TRIANGLE so that
i) order of vowels remains the same
ii)relative positions of vowels and consonants doesnt change..

2. Originally Posted by sudhanshu
how many word with or without meaning can be formed from the letters of the word TRIANGLE so that
i) order of vowels remains the same
ii)relative positions of vowels and consonants doesnt change..
There are $3!=6$ ways to arrange the vowels.
In each 'word' there is only one way for "I_A_E" to appear in that order.
So the answer to i) is $\frac{8!}{6}$.

Now you try part ii).

3. Originally Posted by Plato
There are $3!=6$ ways to arrange the vowels.
In each 'word' there is only one way for "I_A_E" to appear in that order.
So the answer to i) is $\frac{8!}{6}$.

Now you try part ii).
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sir,

i have tried the first part as follows

***** I *****A*****E*****
here * denotes the positions taht can be occupied by 5 consonants

we have 20 positions avlbl for 5 consonants
so they can be arranged in 20P5 ways..

is this method correct ??
plz help me

4. Originally Posted by sudhanshu
***** I *****A*****E*****
here * denotes the positions taht can be occupied by 5 consonants
we have 20 positions avlbl for 5 consonants
so they can be arranged in 20P5 ways..is this method correct ?
I this that is well off the mark.

This is a valid rearrangement: LGEITNRA

Notice the consonants and vowels remain in relative fixed positions.
Do you understand?

5. Originally Posted by Plato
I this that is well off the mark.

This is a valid rearrangement: LGEITNRA

Notice the consonants and vowels remain in relative fixed positions.
Do you understand?
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Sir,

in the second part
we have to keep the relative position of vowels and consonant unchanged

i have tried it as follows

C C V V C C C V
five consonants can be arranged in 5! ways
three consonants can be arranged in 3! ways
so the total no. of ways =5!*3!= 120*6 = 720