Fundamental counting Principle :
Let E1 and E2 are two events. The first event E1 happens in "m" different ways,. After the happening of E1, the event E2 happens in n different ways.
The number of ways that the two events can happens is m "\\times" n
This principle can be extended to three or more events.
Factorial means:
Factorial means the product of an integer and all integers below that required number.
Example:
"4! = 4 \\times 3 \\times 2 \\times 1"
we sometimes divide factorials: When we are trying to find the combinations or permutations, we can use to divide the factorial.
Example:
"\\binom {n} {r } = \\frac {n!}{(n-r)! r!}"
Examples for counting Principle:
(1). If we have 3 shirts and 4 pants, the number of ways wearing these shirt and pant combination is 4 x 3 = 12 ways
(2). There is three cities A, B and C, number of routs from city A to city B is 3 and city B to C is 4 ways.
Total number of ways to go from city A to city B = 3 x 4 = 12
Fundamental Rules
we can use the fundamental rule of multiplication, if we have independent events.
We can use the fundamental rule of addition, if we have dependent events.
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