There are N<=10 people.

I'm trying brute force way of approaching the above problem and want to know the time complexity.
Like, for every t-shirt I'm trying to assign it a person(there can be many) and after assigning a person to this t-shirt, I'm recursing for next t-shirt and doing the same until I'm done with assigning all the people.
How can I evaluate the time-complexity from here?

I think it is O(answer)

what's "answer"?

Answer to the test

If your program printed 1000, it made approx. 1000 leaf recursion calls

Is there a way to generalise the no. of recursive calls. For eg - Assuming that there are 10 people and each person has 1 to 100 t-shirt. How do we evaluate the time-complexity for this?

In worst case each person can wear all 100 shirts.
Complexity on such test will be
100 * (100 - 1) * (100 -2 ) * ... * (100 - N + 1) recursive calls

K := 100

we get (factorial(K) / factorial(K-N)) calls.
It should be multiplied by time spent in one call, e.g. O(K)

Isn't it something like no. of ways of distributing r things(t-shirts) to n people which is => C(n+r-1, r-1) ?

in the case where each person can wear all 100 t-shirts

C(n+r-1, r-1) is another formula, it does not help in this problem.
E.g. consider N=101.
Answer is, obviously, 0.
But C(101+100-1, 100-1) is nonzero

i think, it holds true for the case where r>N

well, N = 3, r = 5.
Answer is 5! / 2! = 120/2 = 60.
C(3+5-1, 5-1) = C(7, 4) = 35.

C(n+r-1, r-1) is number of ways to express R as sum of N non-negative numbers.

Yes, that's a way. Let's think  it the other way. Recursing over all t-shirts and for each t-shirt choosing only those people who have not been assigned a t-shirt till now. So, I start with the first t-shirt and iterate  over all the eligible people who can wear it. Then after assigning a t-shirt to one of the person, we recurse for the next t-shirt and assign the 2nd t-shirt to some eligible person(also this person shouldn't have been assigned a t-shirt in the previous recursions) and do this until all person are assigned a t-shirt. Also, for a t-shirt there can be no person who is assigned this t-shirt(because for eg- if we have 100 t-shirts and 10 people then there are 90 t-shirts which aren't worn by anyone).

How do I assess the time-complexity for goins this way?

it is still O(Answer)

Any lower bound?

Answer can be 0 - ~10^100, so it only depends on the answer how mush steps it will take (I think)

something like CollectionSize(1) * CollectionSize(2) * .... * CollectionSize(N)