Final answer:
To calculate the probability of getting either four number cards or four face cards when pulling 5 cards without replacement from a standard deck of 52 cards, you can use the concept of combination. Calculate the number of ways to select 4 number cards and 4 face cards separately, and then divide the sum of these two cases by the total number of possible outcomes.
Step-by-step explanation:
To calculate the probability of getting either four number cards or four face cards when pulling 5 cards without replacing them, we need to consider the total number of cards in the deck.
In a standard deck of playing cards, there are 52 cards.
The deck consists of four suits (clubs, diamonds, hearts, and spades), with 13 cards in each suit.
To calculate the probability, we can use the concept of combination. The formula to calculate the combination is:
C(n, r) = n! / (r!(n-r)!)
For the case of getting four number cards:
Number of number cards: 36 (4 suits * 9 number cards per suit)
Number of ways to select 4 number cards from 36: C(36, 4)
For the case of getting four face cards:
Number of face cards: 12 (4 suits * 3 face cards per suit)
Number of ways to select 4 face cards from 12: C(12, 4)
The total number of possible outcomes when drawing 5 cards without replacement is C(52, 5).
To calculate the probability, we divide the favorable outcomes by the total number of outcomes:
P(favorable) = (C(36, 4) + C(12, 4)) / C(52, 5)
Now, you can calculate the probability using the formula mentioned above.