Questions: Selecting Musicals How many different ways can a theatrical group select 4 musicals and 2 dramas from 11 musicals and 11 dramas to be presented during the year? The total number of different ways to select 4 musicals and 2 dramas is

Solution Steps

To find the number of ways to select 4 musicals from 11, we use the combination formula:

\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]

where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose. For the musicals:

\[ \binom{11}{4} = \frac{11!}{4!(11-4)!} = \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1} = 330 \]

Similarly, to find the number of ways to select 2 dramas from 11, we use the combination formula:

\[ \binom{11}{2} = \frac{11!}{2!(11-2)!} = \frac{11 \times 10}{2 \times 1} = 55 \]

The total number of ways to select 4 musicals and 2 dramas is the product of the two combinations:

\[ \binom{11}{4} \times \binom{11}{2} = 330 \times 55 = 18150 \]

Final Answer