Question

The maximum number of different permutations of 4 letters of the word "EARTHQUAKE" is-

• A. 2910
• B. 2550
• C. 2190
• D. 2091

Answer 1

The correct option is D 2091

Case :- All $4$ letter different

Total no of different letters $8$

$4$ word letters formed by there $8$ different letters

$=8c_4\times 41=\frac{8\times 7\times 6\times 5}{24}\times 4$

$=1680$

Case : - $2$ same & $2$ different from the other $6$ different letters $4$ word letters formed by this case

$\frac{2c_1\times 7c_2\times 4!}{2!}$

$=504$

Case :- $

$2$ same & $2$ same

i.e., with $2A^{\prime }s$ and $2E^{\prime }s$

$4$ word letters formed by this case $=\frac{4!}{2!2!}$

$=6$

Total number of ways $+1680+504+6=2190$