Probability question (1 Viewer)

[vennyra]

Please help...

All the letters of the word ENCUMBRANCE are arranged in a line. Find the total number of arrangements, which contains all the vowels alphabetically in order but separated by at least one consonant.

Thanks in advance

 

[Fosweb]

I'm pretty sure this came up before. Search the 4U forum maybe?

 

[crazylilmonkee]

no idea.. i cant do it

 

[vennyra]

Originally posted by Fosweb
I'm pretty sure this came up before. Search the 4U forum maybe?

Thankyou so much... i did a quick search and found this thread: http://www.boredofstudies.org/community/showthread.php?s=&threadid=12398

 

[compower1]

wow is this really 3unit?

 

[ricenoodles]

.

 

[mercury]

The answer is 7! x 8C4

You have four vowels: aeeu
you don't need to arrange them, they have to be in that order

You have 7 consonants: bccmnnr
The number of ways of arranging them = 7!/2!2!

Imagine you space out these consonants in one line

| X | X | X | X | X | X | X |

with X representing consonants and | representing places the vowels can go into

as you can see there are eight such spaces "|", so there are 8 slots the four vowels can go into.

Total number of ways
= 8C4 ways of slotting in the vowels with at least one consonant between every two vowels x number of ways arranging consonants

= 8C4 x 7!/2!2!
= 88200

 

[mercury]

Originally posted by Fosweb
I'm pretty sure this came up before. Search the 4U forum maybe?

oh yeah... sique mentioned that before in the other thread i think.