Permutations with Special Arrangements

[Guest]

Using the letters in the word " square ", tell how many 6-letter arrangements, with no repetitions, are possible if the :

a) first letter is a vowel.

b) vowels and consonants alternate, beginning with a consonant.

 

[soroban]

Hello, interval!

Using the letters in the word SQUARE, how many 6-letter arrangements,
with no repetitions, are possible if:

a) the first letter is a vowel.

b) vowels and consonants alternate, beginning with a consonant.

a) The first letter is a vowel.
There are 3 choices of a vowel for the first letter.
The remainin 5 letters can be arranged in 5! ways.
. . Answer: \(\displaystyle \,\) 3·5! = 360 arrangements.

b) The arrangement is: \(\displaystyle \,CVCVCV\)
The three constants can be placed in 3! ways.
The three vowels can be placed in 3! ways.
. . Answer: \(\displaystyle \,\) (3!)·(3!) = 36 arrangements.

 

[Guest]

ok

Thank you soroban.