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A theater director needs to cast three male roles in the school pley, with each heving different lines, If ten students Buci tion for these parts, how many different ways are there for the director to cast these roles?

Step by step solutions

10 x 9 x 8 = 720 different ways

Did you know?

Did you know that the number of different ways a theater director can cast three male roles with different lines from ten students auditioning is calculated using the concept of permutations? Permutations are arrangements of objects where the order matters. In this case, the order of casting the roles matters, as each male role has different lines. To find the number of permutations, we use the formula for evaluating permutations of n objects taken r at a time, which is given by nPr = n! / (n-r)!. Applying this formula to our scenario, with ten students auditioning for three roles, we get 10P3 = 10! / (10-3)! = 10! / 7! = (10 * 9 * 8) / (3 * 2 * 1) = 720. Thus, there are 720 different ways for the director to cast these three male roles.