Probablities

[birty99]

Hi

Could anyone help me with the following problem or point me in the right direction?

If I had a combination lock with 10 digits but I knew 2 digits were "A", 4 digits were "B", 1 digit was "C" and the remaining 3 digits were "D". What are the total number of unique combinations?

I don't need the actual answer but a formula to work it out!

e.g.

3 digit combination lock

if 3 digits were "A" that would be 1 unique combination.

if 1 digit was "A" and 2 digits were "B" that would be 3 unique combinations.

if 1 digit was "A", 1 digit was "B" and the remaining digit was "C" that would be 6 unique comination (1 x 2 x 3)

Any help would be appreciated!


Andrew

 

[galactus]

The number of different arrangements when we have repeats. This is a mulltinomial.

There are 10 letters, so there are 10! arrangements.

But, we have repeats. \(\displaystyle \frac{10!}{2!4!3!1!}\)

is the number arrangements with the given conditions.