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High School Mathematics - 2
7.12 Fundamental Counting Principle

Fundamental Counting Principle
Example 1: Let there be three jobs a, b, c and three persons A, B and C. Find the possible number of assignments of jobs so that one person is assigned only one job.
Solution: Let us start with person A. A can be assigned the remaining jobs in the way shown in the following tree diagram as shown below

The first set of branches of the tree shows that A can be assigned any one of the three jobs(a, b, c). Then for each one of these we can assign either of the two remaining jobs to B shown by the second set of branches of the tree. For each one of these two jobs there is only one job left at the end, which can be assigned to C.
The persons A, B and C can be assigned the three jobs a,b,c in six different ways as shown.

Directions: Solve the following.
Q 1: John wants to go abroad by ship and return by air. He has a choice of 6 different ships

Q 2:

Q 3:

Q 4:

Q 5:

Q 6:

Q 7: There are 5 routes from place A to place B and 3 routed from place B to place C. Find how many different routes are there from A to C via B.

Q 8:

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Question 10: This question is available to subscribers only!

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