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