Question

How many different words can be formed with the letters AAAABBCCD (not necessarily meaningful words)?

Answer 1

Answer:

3780 different words

Step-by-step explanation:

The number of possible words that can be formed by a word with n letters is given by n! (factorial of n), but when we have repeated letters, we need to divide the result by the factorial of each number of repeated letters.

In this case, we have 9 letters, but we have 4 times A, 2 times B and 2 times C, so the formula to calculate the number of different words is:

$number = {9!}/(4!2!2!)$

$number = (9*8*7*6*5*4*3*2)/(4*3*2*2*2)$

$number = 3780\ words$

So we can form 3780 different words.