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A group of 25 singers is auditioning for a cast of 10 spots in a Broadway show. How many distinct casts are possible? (Assume the order of selection is unimportant.)

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Final answer:

The number of distinct casts possible for a Broadway show selecting 10 singers out of 25 can be calculated using the combination formula.


Explanation:

To calculate the number of distinct casts possible when selecting 10 singers out of 25 for a Broadway show, we use the concept of combinations.

The formula for combinations is:

C(n, r) = n! / (r! (n-r)!)

where n is the total number of items and r is the number of items to be selected.

In this case:

Therefore, C(25, 10) = 25! / (10! 15!) = 3,268,760.

So, there are 3,268,760 distinct casts possible for the Broadway show.


Learn more about Combination formula in Mathematics here:

https://brainly.com/question/3242724


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