ASSASSINATION ==> 13 letters ===> N(S) = 4, N(A) = 3, N(N) = 2, N(I) = 2, N(O) = 1, N(T) = 1
Here we will use the concept of selection + arrangement.
Case 1: All four letters are different
$\binom{6}{4}*4!$ ( Selecting fours letters from 6 different letters and arranging them) = 360
case2: 2 same , 2 different.
$\frac{\binom{4}{1}\;*\;\binom{5}{2}\; *\; 4\;!}{2\;!}$ = 480
case3: 2 same , 2 same
$\frac{\binom{4}{2}\; *\; 4\;!}{2\;! \; * \;2\;!}$ = 36
case 4: 3 same , 1 different
$\frac{\binom{2}{1} \;*\; \binom{5}{1} \;*\; 4!}{3\;!}$ = 40
case 5: 4 same
$\frac{\binom{1}{1} \;*\; 4!}{4\;!}$ = 1
Total = 360 + 480 + 36 +40 + 1 = 917
