Tell me in how many ways you (A) and your brother (B) can sit in two chairs before the TV?
2 ways, right?
AB and BA.
Now, you (a), your dad (b) and your mom (c) can sit in three chairs in how many ways?
Hmm, interesting but thoughtful!
Here it is:
abc, acb, bac, bca, cab, cba.
First, you occupy the first chair. Ask your dad and mom to exchange the other two seats in two ways.
Now, its your dad’s turn in the first chair. Now, you and mom will exchange the other two chairs in two ways.
Last, your mom will lead. Like to exchange seats with your dad in two ways? Try it anyway!
So, how many?
Six, in all.
Made it? Yes, you did!
Now, face this. More stuff to dig your brains deep
What if your teeth-grinder brother (d) joins in?
Hmm, big trouble? But, no escape!
You must let in your parents’ other half.
See how many ways you, your brother, your dad and your mom can sit in four chairs?
Here goes the list of
How many totally? My god! 24. That’s too many. Right? Ok.
Now I won’t ask you to add your friend Joe too.
Each of the above 24 sequences is called a permutation.
Permutations are also called arrangements.
We say 4 different persons denoted by letters a, b, c and d can be arranged in 24 ways.
We use a formula to find this. Including the formula, we learn other numerous cases in which the formula will be applied to produce various other formulas
If you wish to set off with your lesson on Permutations and Combinations, then click on the link below:
Permutations and Combinations
Or, if you wish to capture a terse overview of each Permutations and Combinations Formula, then go through each of the following header-links. You can also click the header-links to take you to the page on the specific Permutations and Combinations formula:
Fundamental Rule of Counting:
If there are m ways of doing one task, and n ways of doing another task, then the two tasks can be done one after other in m × n ways.
Factorial of n,n!
the number of ways in which n different things can be arranged by taking all at a time, when each thing can appear only once in every arrangement is called Factorial of n, denoted as n!
Each of the arrangements represented by n! is called a permutation.