Answer:
(n+9)!/(n!9!)
Step-by-step explanation:
A combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.
This is a case of combination with repetition because any n-digit sequence can have numbers repeated. For example in the sequence 00238899 there are 2 zeros.
The formula to find the number of combinations when repetition is allowed is:
(n+N-1)!/[n!(N-1)!]
where
N is the number of elements of the set we can choose from
n is the number of elements we choose
In this case, the set {0,1,2,3,4,5,6,7,8,9} has 10 elements, N=10
The number of n-digit sequences is given by
(n+10-1)!/[n!(10-1)!]=(n+9)!/(n!9!)
