Question

The number of ways of arrangement of letters of the word 'Delhi' if $e$ always comes before ${}^{\prime }{i}^{\prime }$ is

• A. $62$
• B. $34$
• C. $33$
• D. $60$

Answer 1

The correct option is A $62$

E in first place - remaining $4$ places arranged -$4!$ ways

E in $2^{nd}$ place - First place by $3$ letters & remaining $3$ places arranged in $3!$ ways -$3\times 3!$

E in $3^{rd}$ place- first $2$ places arranged $3\times 2$ ways and last $2$ places arranged in $2!$ ways $5-6\times 2!$

E in $4^{th}$ place, the first $3$ places arranged in $3!$ ways

$\therefore$ Total $=4!+3\times 3!+6\times 2!+3!=24+18+12+6$

$=60$ ways.