Shakespeare is credited with writing 37 plays, of which 11 are tragedies, 16 are comedies and 10 are histories. Determine the number of different ways you could choose to read 3 tragedies and 2 comedies??
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To determine the number of different ways you could choose to read 3 tragedies and 2 comedies, you can use the combination formula. The combination formula calculates the number of ways to choose a specific number of items from a larger set, without regard to the order in which they are chosen.
The formula for calculating combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where:
C(n, r) represents the number of combinations of n items taken r at a time.
n! represents the factorial of n (n factorial).
r! represents the factorial of r.
(n-r)! represents the factorial of n-r.
In this case, we want to calculate the number of ways to select 3 tragedies from the 11 available and 2 comedies from the 16 available.
Using the combination formula, we have:
C(11, 3) * C(16, 2) = (11! / (3! * (11-3)!) * (16! / (2! * (16-2)!))
Simplifying these factorials, we get:
(11! / (3! * 8!)) * (16! / (2! * 14!))
Canceling out the common factors:
(11 * 10 * 9 / (3 * 2 * 1)) * (16 * 15 / (2 * 1))
Evaluating further:
(990 / 6) * (240 / 2)
Simplifying:
165 * 120
Therefore, there are 19,800 (165 * 120) different ways to choose to read 3 tragedies and 2 comedies from the given collection of plays.