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Fundamental principal of counting
☼ Fundamental principal of counting : Let us consider the following situation. A man has two shirts and three trousers.
S1 S2 T1 T2 T3
If he wears S1, he can either wear T1 or T2 or T3. This means that for every shirt, he has a choice of three trousers. Thus, for two shirts, he has a total of 2 3 = 6 ways in which he can dress up. This is represented as :
S1T1 S2T1
S1T2 S2T2
S1T3 S2T3
Let’s consider the following examples.
e.g. (i) I can go from Mumbai to Chennai via three routes – road, rail or air. From Chennai to Delhi, I have the choice of taking either or two modes – road and air. If I have to go from Mumbai to Delhi via Chennai, in how many ways can I make the journey ?
Solution.
From Mumbai to Chennai, there are three modes, say m = 3. From Chennai to Delhi there are two modes, say n = 2.
Total number of ways = m n = 3 2 = 6 ways.
(ii) How many three-digit numbers can be formed using the digits 1, 2, 3, 4 ?
Soln.
|
Hundredth Place |
Tenth Place | Unit Place |
| Can use : 1, 2, 3, 4 | Can use : 1, 2, 3, 4 | Can use : 1, 2, 3, 4 |
| 4 ways | 4 ways |
4 ways |
Total no. of three digit nos. using the digits 1, 2, 3, 4 = 4 4 4 = 64
