Final answer:
The student must calculate the probability of a specific eight card hand from a standard deck. The probability is the number of favorable outcomes divided by the total number of possibilities, with the numerator staying at 4 in its simplest form.
Step-by-step explanation:
The student is asked to calculate the probability of being dealt an eight card hand from a standard deck of 52 playing cards where the hand consists of consecutive cards (A, 2, 3, 4, 5, 6, 7, 8) from the same suit. Since there are four suits and the question asks for the hand to be from any one of those suits, there are four favorable outcomes (each suit represents a possible outcome). To find the single hand of eight specific cards of the same suit, there would only be one way to pick that exact sequence from that specific suit.
The total number of different hands that can be dealt is the combination of 52 cards taken eight at a time, which is calculated using the formula for combinations C(n, k) = n!/(k!(n-k)!), where n is the total number of cards and k is the number of cards in the hand:
C(52, 8) = 52!/(8!(52-8)!) = 52!/(8!44!).
Therefore, the probability of getting that specific hand, in its lowest terms, is 4 (the four favorable outcomes, one for each suit), divided by C(52, 8), the total number of different eight card hands that can be dealt from the deck.
The fraction can be simplified but the numerator in its most simplified form will remain 4 since it can't be divided further. Thus, in the fraction form of the probability, the numerator a is 4.