g decks to draw a specific card by a certain turn. For this problem you will be calculating the probability of drawing at least one copy of a specific card by a given turn. Here's how our card game will be played 1. You will initially draw N cards from your deck. This is your starting hand 2. The next step is the mulligan. In the mulligan step you select between 0 and N cards to set aside. Let the number of cards you choose to set aside be M. You will then draw M more cards from the deck. 1. Note. You cannot redraw the cards you set aside because you set them aside and did not place them back into the deck 3. You then shuffle those cards back into the deck 4. After the initial draw and the mulligan you draw one card per turn. So now we want to calculate what are the odds that you will get at least one copy of the card you are looking for by the desired turn. Note that we are actually calculating the probability in this problem and