Exercise 9. We have a deck containing 52 cards. Each card has a value among "1, 2, $3,4,5,6,7,8,9,10$, jack, queen, king" and a suit among "hearts, diamonds, spades, clubs," such that for each value and each suit, the deck contains a unique card with that value and that suit. A hand of 5 cards is a selection of 5 cards from this deck, without regard to the order in which the cards are chosen. How many hands of 5 cards contain four cards of the same value?

Only a numerical answer is expected here.
Solution to Exercise 9 To choose a hand of 5 cards where 4 cards have the same value, you first need to choose the value in question. There are 13 choices for this since there are 13 values. There are then 48 choices for the fifth card. Therefore, in total, there are $13 \times 48 = 624$ possible hands.

Grader Comments The exercise was successfully completed by the majority of students. The main errors were forgetting the suit of the last card (for those who found 156), or even forgetting the last card entirely (for those who found 13). Some misunderstood the problem, trying to count the number of possible hands simultaneously. Finally, several made mistakes in the final calculation of $13 \times 48$, which is a pity.