In Adler and Ross 'Coupon subset collector problem' 2001, the following formula (7) is stated:

Assuming I have a constant subset size > 1, can I get the expected number of draws to get the last n from s coupons by using formula (7) and simply summing from n. For example, if there are s=10 distinct coupons, if I want to find how many draws to collect the last n=5 distinct types, and each draw has m=3 coupons, can I sum from j=6 to s=10 to get the correct answer.

Thanks in advance.