In how many different ways can the letters of the word ALLAHABAD be arranged?

Solution (By Examveda Team)

The given word contains 9 letters, namely 4A, 2L, 1H, 1B and 1D.
∴ Required number of ways
$$\eqalign{ & = \frac{{9!}}{{4! \,2! \,1! \,1! \,1!}} \cr & = \frac{{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{4 \times 3 \times 2 \times 1 \times 2}} \cr & = 7560 \cr} $$