Five boys and 6 girls would like to serve on the homecoming court , which will consist of 2 boys and 2 girls.How many different homecoming courts are possible ?

Options

A. 30
B. 61
C. 150
D. 900

Explanation

To solve the problem of how many different homecoming courts can be formed with 2 boys and 2 girls from a group of 5 boys and 6 girls, we can follow these steps:

### Step 1: Calculate the number of ways to choose 2 boys from 5 boys.
We can use the combination formula \( C(n, r) = \frac{n!}{r!(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

For choosing 2 boys from 5:
\[ C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5!}{2! \cdot 3!} \]
Calculating this gives:
\[ = \frac{5 \times 4}{2 \times 1} = 10 \]

### Step 2: Calculate the number of ways to choose 2 girls from 6 girls.
Using the same combination formula for choosing 2 girls from 6:
\[ C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2! \cdot 4!} \]
Calculating this gives:
\[ = \frac{6 \times 5}{2 \times 1} = 15 \]

### Step 3: Multiply the number of combinations of boys and girls.
Since we need to choose both boys and girls, we multiply the number of ways to choose the boys by the number of ways to choose the girls:
\[ \text{Total combinations} = C(5, 2) \times C(6, 2) = 10 \times 15 = 150 \]

### Final Answer:
Thus, the total number of different homecoming courts possible is **150**.

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