Question

$\text{Let us consider the word 'MOTIHARI'. Six letters are choosen from the given word and}\text{arranged in all possible ways to form a new word (may be meaningful or non-meaningful),}\text{then the number of new words so formed are}$

• A. $10440$
• B. $11440$
• C. $9440$
• D. $12440$

Answer 1

The correct option is A $10440$

$\text{Here the letter 'i' is reapeated twice. So, there will be 3 cases.}$

$\text{case 1: No 'i' comes:}\text{remaining words are 6. From which we have to make}\text{6 letter words =}{}^6{C}_6\cdot 6!=720$

$\text{case 2: Exactly one 'i' comes:}\text{remaining words are 6. From which we have to select}\text{5 letters. So the total number of words =}{}^6{C}_5\cdot 6!=4320$

$\text{case 3: Exactly two 'i' come:}\text{remaining words are 6, From which we have to select}\text{4 letters. So the total number of words =}{}^6{C}_4\cdot \frac{6!}{2!}=5400$

$\text{total}=10440$