5 actors and 8 actresses are available for a play which required 3 male and 4 female find the number of different possible cast lists
5C3 * 8C4
[(5 * 4) / (2 * 1)] * [(8 * 7 * 6 * 4) / (4 * 3 * 2 * 1)]
Well, let's do some casting calculations! We need to select 3 male actors from a pool of 5, and 4 female actresses from a pool of 8. To calculate the number of different possible cast lists, we can use the combination formula.
The number of ways to choose 3 male actors from 5 would be C(5, 3), which can be calculated as:
C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3) / (3 * 2 * 1) = 10
Similarly, the number of ways to choose 4 female actresses from 8 would be C(8, 4), which can be calculated as:
C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70
Now, to find the total number of different cast lists, we need to multiply these two results together:
Total number of cast lists = C(5, 3) * C(8, 4) = 10 * 70 = 700
Therefore, there are 700 different possible cast lists for this play. Which means there are 700 opportunities for both chaos and laughter on stage!
To find the number of different possible cast lists, we need to calculate the number of combinations of actors and actresses that satisfy the requirements of the play.
First, let's select the 3 male actors out of the available 5. This can be done using the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of available actors, and r is the number of actors required.
For the male actors: C(5, 3) = 5! / (3!(5-3)!) = 10
Next, we need to select the 4 female actresses out of the available 8. This can also be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
For the female actresses: C(8, 4) = 8! / (4!(8-4)!) = 70
Finally, to find the total number of different possible cast lists, we multiply the number of combinations for male actors with the number of combinations for female actresses:
Total number of cast lists = 10 * 70 = 700
Therefore, there are 700 different possible cast lists.
To find the number of different possible cast lists, we can use combinations.
Since the play requires 3 male actors and 4 female actresses, we need to select 3 males from the available 5 actors and 4 females from the available 8 actresses.
First, let's calculate the number of ways to select 3 males from the 5 available actors. This can be done using combinations:
C(5, 3) = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3) / (3 * 2) = 10
So there are 10 possible ways to select 3 males.
Next, let's calculate the number of ways to select 4 females from the 8 available actresses:
C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2) = 70
So, there are 70 possible ways to select 4 females.
To find the total number of different possible cast lists, we multiply the number of ways to select the males (10) by the number of ways to select the females (70):
Total number of cast lists = 10 * 70 = 700
Therefore, there are 700 different possible cast lists for the play.