probability - Coupon collector problem with partial collection of a specific set of coupons

I am very new in probability and combinatorics and have a naive question around a variation on the coupon collector problem with partial collection.

Lets assume we have a box with 45 coupons labeled 1-45. Now in this case I would like to adjust the CCP such that I can calculate the expected value (amount of draws necessary) to collect 10 specific items. For example item 1-10. How do I adjust my model such that I can calculate the amount of draws necessary to collect each item n times.

I assume that I have to adjust CCP2 in following post (Coupon Collector's Problem with Partial Collections and Coupon Packages) to include the probability that I catch one item is 10/45.

All tips and tricks are welcome!

Thanks for your help