Coupon collector's problem

Hey kiddo! Have you ever collected stickers or cards? Imagine you are collecting 5 different stickers from a pack of 20. You have to keep buying packs until you have collected all those 5 different stickers.

Now, let me tell you about the coupon collector's problem. It is a mathematical problem that asks, "How many packs do you need to buy to collect all the stickers?"

The answer is not so easy because every time you buy a pack, there is a chance that you might get a sticker that you've already collected. So, you have to keep buying packs until you get all the 5 different stickers.

This problem is important to mathematicians because it can help them figure out how long it might take to collect all the stamps, coins, or other collectibles that people are trying to complete their collection.

To solve the coupon collector's problem, we can use a formula that will help us estimate the number of packs needed to complete the collection. The formula is N ≈ m * (ln m + γ) where N is the number of packs needed, m is the number of different stickers, and γ is a mathematical constant.

Now, if we go back to our example, we have m=5 different stickers out of 20. Using the formula, we can estimate that we need about 16 packs to collect all 5 stickers.

So, be patient little one! Keep collecting your stickers and remember that it might take some time to complete your collection, but the satisfaction of completing it will be totally worth it!