in how many ways cold the letters in the word "storage" be arranged if the
vowels must remain in
a)even positions?There are three vowels {o,a,e} and 4 consonants {s,t,r,g}
These would would have the form
CVCVCVC
where C represents a consonant and V a vowel.
Answer 4!3! = 144 ways.b)odd positions?
There are 4 odd positions, 1st, 3rd, 5th, and 7th.
Thats 4C3 = 4 ways to choose the positions for
the vowels: VCVCVCC, VCVCCCV, VCCCVCV, CCVCVCV
For each of these 4 ways there are 4!3! = 144 ways to arrange them.
Answer: (4C3)(4!3!) = 4(144) = 576.
Edwin