Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# 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.

Relevance
• 1 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

120 arrangements

• atsuo
Lv 6
1 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 .