When a person buys 15 boxes, there are 5 cards in the box, and the types of the 5 cards are different from each other (however, the relationship between the cards in the box and other cards in other boxes is uncertain, that iss random). This person wants to collect all types of cards (that is, 45 types) by buying these 15 boxes. Now, please work out the probability of his success.
2026-02-24 17:35:04.1771954504
Probability problems associated with collecting all types of cards
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You can work out the problem using inclusion-exclusion, focusing on the missing cards
The needed probability will be
$1 - P$(at least one card missing - at least 2 cards missing + .....)
and the Pr of at least k cards missing is
$= \dbinom{45}{k}\left[\dbinom{45-k}{5}\right]^{15}\bigg{/}\left[\dbinom{45}{5}\right]^{15}$