collecting at least 2 (two) coupons of each kind from a set of coupons. One (1) coupon at a time.

Coupons can be different types of items as in collecting at least 1 of each coupon.

example: roll a standard die (1d6)

How many rolls on average to get at least 2 of each face?

N = 6 (coupons = 6)

answer will be less than 2 times that of collecting at least 1 coupon.

answer: 24.1339

Excel sheet below for coupons=6 and k sets=2 (at least 2)

a udf was used to raise the matrix to a power to arrrive at the distribution (pmf)

R code to follow soon (working on)

below sheet is for the average draws to collect 'at least 1' and 'at least 2' sets of N coupons up to 1000 coupons. Above 600 is an approxamation value for 'at least 2'