How many ways we arrange the word 'allahabad'?

Answer 1

The word "allahabad" consists of 9 letters, with the letters 'a' appearing 3 times, 'l' appearing 1 time, 'h' appearing 1 time, 'b' appearing 1 time, and 'd' appearing 1 time. The total number of arrangements can be calculated using the formula for permutations of multiset:

[ \frac{n!}{n_1! \cdot n_2! \cdot ... \cdot n_k!} ]

In this case, it is

[ \frac{9!}{3! \cdot 1! \cdot 1! \cdot 1! \cdot 1!} = \frac{362880}{6} = 60480. ]

Thus, there are 60,480 distinct ways to arrange the letters in "allahabad."