all the letters of a word krishna are used to form a seven letter word then the no of words which begin and end with a vowel are

The no. of vowels in the word are 2. They can be arranged in 2! ways. They can again be arranged in two ways in the beginning and one in the end. So we are left with 5 places which can be taken by any of the nonvowel in 5 ways. Therefore requit no. of ways = 2! × 5!. Number of given letters = 7Total no. of words can be formed = 7!So, required probability= 2!×5!/7!