Question

Management selection A corporation plans to fill 2 different positions for vice-president, V, and V2, from administrative officers in 2 of its manufacturing plants. Plant A has 5 officers and plant B has 7a. How many ways can these 2 positions be filled if the V, position is to be filled from plant A and the V, position from plant B?b. How many ways can the 2 positions be filled if the selection is made without regard to plant?

Answer 1

a) In this case, we have 5 options for V1 and 7 options for V2.

This means that for every one of the 5 officers that can be picked as V1, there are 7 combinations in V2.

Then, we can calculate all the possible combinations as 5*7=35.

There are 35 ways these 2 positions can be filled.

b) If we don't take into account the plant, we have 5+7=12 options for V1.

Then, for each selection of V1 we have 12-1=11 options for V2, as we are not selecting the same person for both positions.

This is like selecting names from a group without replacement. For the first position, we can select any of the 12 options we have.

For the second position, we have only 11 left to pick.

Then, for each of the 12 options for V1, we will have 11 options for V2, so we have to multiply these numbers in order to calculate the number of ways.

We can calculate all the possible combinations as 12*11=132.

There are 132 ways these 2 positions can be filled if the selection is made without regard to the plant.