How many different 10-letter arrangements can be made

Question

How many different 10-letter arrangements can be made from the word BASKETBALL?

1. 36288012
2. 453600
3. 604800
4. 26300

Answer 1

There are 10 letters of which there are:

2-A's

2-B's

2-L's

4-single letters left

Number of arrangements = C(10,2)C(8,2)C(6,2)4! = (10!/(2!8!))(8!/(2!6!))(6!/(2!4!))4! = 10!/8 = 3628800/8 = 453600

Answer (2)