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 four cards are selected from a set of seven Tarot cards?
Thank you
not combinations because order does not matter in combinations
we need permutations of 7 taken 4 at a time
p(n,r) = n!/(n-r)!
= 7!/3!
= 7*6*5*4 = 840
Thank you very much
To determine the number of different readings possible when four cards are selected from a set of seven Tarot cards, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
n = total number of items (Tarot cards)
r = number of items being selected (in this case, 4)
Using the formula, we can calculate the number of different readings:
C(7, 4) = 7! / (4!(7-4)!)
C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3 * 2 * 1)
C(7, 4) = (7 * 6 * 5) / (3 * 2 * 1)
C(7, 4) = 35
Therefore, there are 35 different readings possible when four cards are selected from a set of seven Tarot cards.
To determine the number of different readings possible when selecting four cards from a set of seven Tarot cards, we can use a combination formula.
In this case, we want to select four cards out of a pool of seven with no regard to the order in which they are chosen. The formula for combinations is:
C(n, r) = n! / r!(n-r)!
Where n is the total number of items to choose from, and r is the number of items to choose. In our case, n=7 (seven tarot cards) and r=4 (four cards to be selected).
Plugging the values into the combination formula, we get:
C(7, 4) = 7! / 4!(7-4)! = 7! / 4!3!
Now let's simplify this expression:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
Substituting these values back into the formula:
C(7, 4) = 5040 / (24 x 6) = 5040 / 144 = 35
Therefore, there are 35 different readings possible when selecting four cards from a set of seven Tarot cards.