In a drama workshop, there are 6 actors who would like to appear in a scene. However, the scene has only 5 different roles. Each role can be played by anyone, and no actor can play more than one role. How many different casts are possible?
Question
In a drama workshop, there are 6 actors who would like to appear in a scene. However, the scene has only 5 different roles. Each role can be played by anyone, and no actor can play more than one role. How many different casts are possible?
Solution
To solve this problem, we can use the concept of permutations in combinatorics.
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula:
P(n, r) = n! / (n-r)!
where "!" denotes factorial, which is the product of all positive integers up to that number.
In this case, we have 6 actors and 5 roles, so we want to find the number of permutations of 6 objects taken 5 at a time.
P(6, 5) = 6! / (6-5)!
= 65432*1 / 1
= 720
So, there are 720 different casts possible for the scene.
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