Rule of Sum
If one experiment has n possible outcomes and another has m possible outcomes, then there are (m + n) possible outcomes when exactly one of these experiments is performed.
In other words if a job can be done by n methods and by using the first method can be done in a1 ways or by second method in a2 ways and so on ... by the nth method in an ways, then the number of ways to get the job done is (a1 + a2 + ...... + an).
Example:
How many straight lines can be formed from six points, no three of which are collinear?
Solution:
To form a straight line, we need to select two points out of six points. This can be done in 6C2 ways = 6.5/2.1 = 15 ways.
Example:
In how many ways can a committee of five be formed from amongst four boys and six girls so as to include exactly two girls?
Solution:
We have to select two girls from six girls and three boys from four boys.
Number of ways of selecting girls = 6C2 = 6.5/2.1 = 15
Number of ways of selecting boys = 4C3 = 4
Number of ways of forming the committee = 15 × 4 = 60.
Note: Here we have used multiplication rule.
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