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 6 officers and plant B has 8.

a) If the V1 position is to be filled plant A, it can be filled in 6 ways.

b) If the selections are made without regard to plant, the first position can be filled in 14 ways.

**Solution:-**

Multiplication Principle (for Counting)

If two operations O1 and O2 are performed, with N1 possible outcomes for the first operation and N2 possible outcomes for the second operation, then there are

N1* N2

Possible combined outcomes for the first operation followed by the second.

a) If the V1 position is to be filled plant A, it can be filled in 6 ways.

If the V2 position is to filled from plant B, it can be filled is 8 ways.

If the V1 position is to be filled from plant A and the V2 from plant B, there are (6*8) = 48 ways these 2 position can be filled.

b) If the selections are made without regard to plant, the first position can be filled in 14 ways.

If the selection are made without regard to plant, the second position can be filled in 13 ways after the first position is filled.

If the selections are made without regards to plant, the 2 positions can be filled in (14*13) = 182 ways