So, we know that in a combination the order does not matter, and in a permutation the order does matter. Where in the real world are there situations in which we want to know all the possible combinations of things where the order does and does not matter?
Well, what if you biked to school, and realized at the end of the day that you forgot the combination to your three numbered lock using the numbers 0 to 5? Permutations can help you here. If the combination to your lock is 502 then 205 or 520 for example won't work. Using what you know about permutations you can determine how many possible combinations of numbers there are and whether it's worth sitting there and going through them all or if you should just call a locksmith!
Combinations can help you if you want to win the lottery where as long as you pick the right numbers you win! You can find out how many tickets you need to buy to guarantee a win ;)
Permutation is the number of ways you can arrange things. The order of arranging is also considered in permutations.
The combination is the different number of ways we choose. In combination the order is not considered.
Permutation or diffrent ways of arranging 2 marbles red green in 3 places shelves A,B and C.
A B C
r g -
g r -
r - g
g - r
- g r
- r g
The number of arrangements above is 3P2 = 3!/(3-2)! =3!/1! = 3*2 *1 = 6.
In combinations it is the number of diffrent things you select.
The number of two marbles group you can do in this case of 3 diffrent marbles green, blue and red is 3 as the the number of groups you can form are :
Here gr and rb are not different, gb and bg are not different and similarly br and rb are not different.( Whereas , in permutation, gr and rg , gb and bg, and br and rb are treated different).
Can u give 3 examples of permutation and combination in real life?