Questions: 3. A small company has 3 divisions: Sales, Research and Development, and Manufacturing. One person from each division will be chosen to create an advisory board for the management group. If there are 8 people in Sales, 15 in Research and Development, and 48 in Manufacturing, how many different compositions of the advisory board are possible?

Solution Steps

To find the number of different compositions of the advisory board, we need to calculate the product of the number of choices available from each division. This is because the selection of a person from each division is an independent event.

We have three divisions with the following number of people:

• Sales: \( 8 \)
• Research and Development: \( 15 \)
• Manufacturing: \( 48 \)

The total number of different compositions of the advisory board can be calculated using the product of the number of choices from each division: \[ \text{Total Compositions} = 8 \times 15 \times 48 \]

Calculating the product: \[ 8 \times 15 = 120 \] \[ 120 \times 48 = 5760 \]

Final Answer