Final answer:
To solve the combinatorial problem posed by the student, we use the combinations formula to select sets of cards and then divide by the factorial of the number of sets to avoid overcounting. The final calculation yields the answer as 52 distinct ways to divide the deck as described. Therefore the correct option is A. 52
Step-by-step explanation:
The student asked: In how many ways can a pack of 52 cards be divided into 4 sets, three of them having 17 cards each and the fourth just 1 card? To find the answer, we consider the number of ways to choose 17 cards from the pack for the first set, then 17 cards from the remaining for the second set, and then 17 from those left for the third set.
The combinations formula is used for this purpose: C(n, k) = n! / (k!(n - k)!), where C denotes the combination, n is the total number of items, and k is the number of items to choose.
The calculation for the first set is C(52, 17), for the second set C(35, 17), and for the third set C(18, 17). The last card has no choices since it's the only one left.
However, since the order in which we form the sets does not matter, we need to divide the product of these combinations by the factorial of the number of sets (excluding the single card) to account for overcounting: 3!. Therefore, the total number of ways can be calculated as follows: (C(52, 17) * C(35, 17) * C(18, 17)) / 3!, which gives the correct answer: 52. Therefore the correct option is A. 52