Tarot cards are used for telling fortunes, and in a reading, the arrangement of the cards is as important as the cards themselves. How many different readings are possible if five cards are selected from a set of nine Tarot cards?
9P5 = 9*8*7*6*5
To determine the number of different readings possible when selecting five cards from a set of nine Tarot cards, we can use the concept of combinations.
In a combination, the order of selection does not matter, and repetition is not allowed. Each reading will consist of five unique cards.
The number of combinations can be calculated using the formula for combinations:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n is the total number of objects to choose from (in this case, the total number of Tarot cards)
- r is the number of objects being chosen (in this case, the number of cards in each reading)
Applying the formula, we have:
C(9, 5) = 9! / (5! * (9 - 5)!)
Simplifying this expression:
C(9, 5) = (9 * 8 * 7 * 6 * 5!) / (5! * (4 * 3 * 2 * 1))
The factorials cancel out, leaving us with:
C(9, 5) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
Evaluating this expression:
C(9, 5) = 3024 / 24
C(9, 5) = 126
Therefore, there are 126 different readings possible if five cards are selected from a set of nine Tarot cards.