Problem Solving

Combination probs. .. when to MULTIPLY and when to ADD ??

e.g.
To fill a number of vaccancies, an employer must hire 2 programmers from 6 applicants, and 2 managers from 4 applicants. What is the total number of ways in which she can make her selection?

Solu-
Programmers:
= (6!/(3! x 3!))
= 6x5x4 / 3x2
= 20

Managers:
= (4!/(2!x2!))
= 4x3 / 2
= 6

So the total number of ways is -
6x20 = 120
OR
6+20 = 26

??? What's the thumb-rule? easy to remember!

The following rules apply for both combinations/permutations and probability.

When we calculate the # of ways/probability of MULTIPLE events, we MULTIPLY.

When we calcluate the # of ways/probability of ALTERNATIVE events, we ADD.

In your example above, we're selecting programmers AND managers, so we MULTIPLY the individual counts.

If we had to select either programmers OR managers, we'd ADD the individual counts.

To identify multiple events, look for words such as "and", "both" or "all".

To identify alternative events, look for words such as "or", "at least" and "at most".