math exercise 3?
How many ways are there to arrange the letters of the word SHEILA if the vowels have to in alphbetical order? The vowels need not be adjacent with each other. Examples: SHAELI, ASHELI.
- PuzzlingLv 71 month ago
Here's a quick way to solve this.
If there were no restrictions, you could arrange the 6 different letters in 6! = 720 ways
Now for 3 vowels, there are 3! = 6 ways to arrange them, but only 1 is in alphabetical order. From that it follows that only 1/6 of the permutations have the vowels in alphabetical order. Thus divide the prior result by 6.
= 720 / 6
= 120 ways
- atsuoLv 61 month ago
1. Choose 3 positions out of 6 positions for 3 vowels .
There are 6C3 = 20 ways exist .
2. Put A,E,I on chosen 3 positions in this order .
There is only 1 way .
3. Put S,H,L on other 3 positions .
There are 3P3 = 6 ways exist .
So 20*1*6 = 120 ways exist in the total .