Question

The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is

• A. $2454$
• B. $2452$
• C. $2450$
• D. $1806$

Answer 1

Answer: (A)

$2454$

Answer 2

In a word EXAMINATION has $2A,\,2I,\,2N,\,E,\,M,\,O,\,T,\,X,$ therfore 7 letters can be chosen in following ways Case I when 2 alike of one kind and 2 alike of second kind of is
$^{3}{{C}_{2}}$ .
$\therefore$ Number of words ${{=}^{3}}{{C}_{2}}\times \frac{4!}{2!\,\,2!}=18$
Case II when 2 alike of one kind and 2 different ie,
$^{3}{{C}_{1}}{{\times }^{7}}{{C}_{2}}.$
$\therefore$ Number of words ${{=}^{3}}{{C}_{1}}{{\times }^{7}}{{C}_{2}}\times \frac{4!}{2!}$
$=756$ Case III when all are different. ie, $^{8}{{C}_{4}}$ .
$\therefore$ Number of words ${{=}^{8}}{{C}_{4}}\times 4!=1680$
Hence, total number of words $=18+756+1680$
$=2454$