thanks ]]>

Permutations: How many ways ‘r’ kids can be picked out of ‘n’ kids and arranged in a line. There are ‘r’ positions in a line.

Any of the n kids can be put in position 1. So there are n choices for position 1 which is n-+1 i.e. n-1+1.

Any of the remaining (n-1) kids can be put in position 2. So there are n-1 choices for position 2 which is n-+1 i.e. n-2+1.

Similarly there are n-2 choices for position 3 which is n-+1 i.e. n-3+1

And there will be n-+1 choices for rth position. n-r+1. So the total number of ways ‘r’ kids can be picked out of ‘n’ kids and arranged in a line is n*(n-1)*(n-2)*….(n-r+1) = (n!)/ (n-r)!

This is written as P(n,r).

Combination: How many ways ‘r’ kids can be picked out of ‘n’ and just put in a group i.e. no arranging them in a line. So once ‘r’ kids are picked out, it is just considered a single choice.

In the first case, after picking ‘r’ kids we arranged them in line. Each of these arrangements generated a new arrangement. All these arrangements are counted as one one for the second case. Let’s see how many arrangement of ‘r’ kids can be done when we put them in a line.

There are r choices for the first position.

r-1 choices for the 2nd position.

r-2 choices for the 3rd position.

..

1 choice for the rth position.

So after picking ‘r’ kids, we can arrange them in a line in r! ways. All these ways should be counted as one. So

the formula for combination (just picking r kids but not arranging them in a line)

(Number of ways for arranging r kids in a line out of n kids total) ÷ (number of ways of arranging r kids in a line)

[(n!)/ (n-r)!] ÷ r! = (n!)/ [(n-r)!*(r!)] ]]>