Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements, (i) do the words start with P (ii) do all the vowels always occur together (iii) do the vowels never occur together (iv) do the words begin wit

Explanation

total arrangements = `(12!)/(3!2!4!)`

(i) `P -----------`

`= (11!)/(3!2!4!)`

(ii) `= (8!)/(3!2!)*(5!)/(4!)`

(iii) `(12!)/(3!2!4!) - (8!5!)/(3!2!4!)`

(iv) `I ---------- P`

`= (10!)/(3!2!4!)`

answer