Correct Answer - Option 2 : 7560
Concept:
PERMUTATION:
Number of Permutations of ‘n’ things taken ‘r’ at a time:
\({\rm{p}}\left( {{\rm{n}},{\rm{\;r}}} \right) = \frac{{{\rm{n}}!}}{{\left( {{\rm{n}} - {\rm{r}}} \right)!}}\)
Number of Permutations of ‘n’ objects where there are n1 repeated items, n2 repeated items, ….. nk repeated items taken ‘r’ at a time:
\({\rm{p}}\left( {{\rm{n}},{\rm{\;r}}} \right) = \frac{{{\rm{n}}!}}{{{{\rm{n}}_1}!{{\rm{n}}_2}!{{\rm{n}}_3}! \ldots .{{\rm{n}}_{\rm{k}}}!}}\)
Calculation:
ALLAHABAD
A → 4 times
L → 2 times
Required no. of arrangements =
\(\frac{9!}{4!2!}\) = (9 × 8 × 7 × 6 × 5) / 2 = 7560
