permutations and combinations help (1 Viewer)

[kr73114]

How many arrangements of the letters in the word ISOSCELES are possible if the vowels (i.e. I, 0 and E) must be together? how would you do this?

 

[dasicmankev]

The number of arrangements = (6!/3!) x (4!/2!) = 1440

Consider this: Group the vowels (I, O, E, E) together as a single entity. Then we can arrange this entity within the group of letters 6! ways. But note that the there are 3 letter 'S' within this larger group, therefore we need to divide by 3! hence 6!/3! within the larger group. We can then arrange the group of vowels within themselves 4! ways, but note again that the letter E is repeated. Therefore we divide by 2! hence we can arrange the vowels within themselves 4!/2! ways.

To get the final answer we simply multiply 6!/3! and 4!/2! together. Hope this helped.

 

[kr73114]

The number of arrangements = (6!/3!) x (4!/2!) = 1440

Consider this: Group the vowels (I, O, E, E) together as a single entity. Then we can arrange this entity within the group of letters 6! ways. But note that the there are 3 letter 'S' within this larger group, therefore we need to divide by 3! hence 6!/3! within the larger group. We can then arrange the group of vowels within themselves 4! ways, but note again that the letter E is repeated. Therefore we divide by 2! hence we can arrange the vowels within themselves 4!/2! ways.

To get the final answer we simply multiply 6!/3! and 4!/2! together. Hope this helped.

yeh thanks