A sequence of numbers:

0 0 0 0 0 0 1 0 2 1 2 0 3 1 0 2

It is 16 numbers long, consists of nine 0's, three 1's, three 2's and one 3.

How many different sequences of these 0's and 1's and 2's and the one 3 can you create in this 16 bit long number?

My shot:

Four different numbers: 0, 1, 2 and 3.

The length of the sequence is 16.

Among those 16, nine of those are nulls, for every sequence.

Among those 16, three of those are 1's for every sequence.

Among those 16, three of those are 2's for every sequence.

Among those 16, 1 of those is 3 for every sequence.

Alone they can be rearranged:

The nine 0's: 16 - 9+1 = 8 * 9 = 72 times can 0 alone be rearranged.

The three 1's: 16 - 3+1 = 14*3 = 42 times can the 1's be rearranged.

The three 2's: 16 - 3+1 = 14*3 = 42 times can the 2's be rearranged.

The one 3: 16 - 1 +1 = 16*1 = 16 times.

Then I multiply those:

72*42*42*16 =2032128times can this sequence of numbers be rearranged iwthin a 16 bit long number.

Something wrong here?

Not entirely sure on my method...