Question: Management selection. A corporation plans to fill 2 different positions for vice-president, V₁ and…

Management selection. A corporation plans to fill 2 different positions for vice-president, V₁ and V₂, from administrative officers in 2 of its manufacturing plants. Plant A has 9 officers and plant B has 6.

a. How many ways can these 2 positions be filled if the V₁ position is to be filled from plant A and the V₂ position from plant B?

Solution

The problem asks us to determine the number of ways two positions, \( V_1 \) and \( V_2 \), can be filled from plant A and plant B, respectively. First, recognize that: - There are 9 officers available in plant A for the \( V_1 \) position. - There are 6 officers available in plant B for the \( V_2 \) position. For each officer selected from plant A for \( V_1 \), any of the 6 officers from plant B can be selected for \( V_2 \). This is a multiplication problem since each selection is independent. Calculate the total number of ways: \[ 9 \times 6 = 54 \] Thus, there are 54 ways to fill the two positions.