Find the number of permutations of the letters of the word ALLAHABAD.

Question

Question

Answer 1

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