Question

Probability of arranging all the letter of the word "practice " so that the vowels always occupy the even place

Answer 1

PRACTICE has 5 consonants and 3 vowels

Total 8 letters, hence 4 even places

But we only have 3 vowels so first we select 3 places from the 4 with

$\binom{4}{3}$

Multiply by 3! For rearrangement between the vowels

Hence we have 24 ways to arrange vowels

Now for consonants there are 2 C's

Hence rearrangement for these will be

5!/2!

= 60

Hence total cases =

$24 \times 60 = 1440$

Total possible words = 1440

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