Question

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

Answer 1

The number of ways with repetitions between identical letters is $10!$ (you can put any of 10 letter at the first place any of remaining nine on second etc)

word has 3 letters ''t'', which means there are 3! rearrangements between them

word has 3 letters ''s'', which means there are 3! rearrangements between them

word has 2 letters ''i'', which means there are 2! rearrangements between them

So, the total number of rearrangments is ${\frac {10!} {3!*3!*2!}}=50400$