Always remember this basic concept of counting
If one operation can be performed in m ways and a second operation can be performed in n ways, the number of ways of performing both the operations will be m*n and the number of ways of performing either one of the operations will be m+n. So all you need to remember is
1. In case of OR we add
2. In case of AND we multiply
Examples based on above concept:
The routes between cities A, B, C, D, E and F is shown below
1. In how many ways can you travel from City A to City F via city B?
2. In how many ways can you travel from City A to City F via city C?
3. Total number of ways to travel from city A to city F?
Post your answers using comment option.
Note: Not giving options to above questions is intentional, as I don't want you to work from solution to the question
Thanks,
Quant-Master
Posts
Response to question 1:
ReplyDeleteCity A -> City B = 1 way
City B -> City D = 3 ways
City D -> City F = 4 ways
Total City A -> City F via City B = 1 * 3 * 4 = 12 ways
Response to question 2:
City A -> City C = 1 way
City C -> City E = 3 ways
City E -> City F = 2 ways
Total City A -> City F via City C = 1 * 3 * 2 = 6 ways
Response to question 3:
Total City A -> City F = 12 + 6 = 18 ways
That explanation is perfect.
ReplyDeleteWe multiply in the first 2 questions because we have to pass through A AND B AND F.
In the 3rd question we add because we can pass through A --->B (or) C ---->F
Let me know if anybody needs further explanation
Thanks,
Quant-Master