1. What is permutation Formulas permutation Formula Derivation
Cards types Use of permutation in civil engineering
2. In probability and statistics, the permutation is defined as
the : Each of several possible ways in which a set number of things
can be arranged
3. Permutations Repetition allowed Repetition is not
allowed
4. Another defination is : An arrangement of n number of
objects (distinct) taken r at a time in specific order is known as
permutation denoted by ( nP )
5. FORMULA: nP= n! (For the repeating permutation)
6. FORMULA: nP = n! (For non repeating permutation) (n-r)!
7. Lets derive the formula for repeating and non repeating
Permutations : Suppose that we are given n distinct objects and we
wish to arrange r of these objects in a line . Any of the objects
can fill up the first place . when the first place has been filled
by one of the n ways then there are (n-1) objects left for filling
second place .
8. Hence by multiplication rule there will be nx(n-1) ways of
filling up the first two places. There will be (n-2) ways to fill
up the 3rd place . Hence the first three places can be filled up by
nx(n-1)x(n-2) ways. Continuiing this way we get .
9. The last which is the r th place can be filled by the
following: n x(n-1)x(n-2) r factors Note that the first factor is
(n-1+1)=n Second factor is (n-1)=(n-2+1) etc Its clear that the r
th factor is (n-r+1) For each place to be filled. -1 for first
place -2 for second place And so on. For each progressive place to
be filled adding +1 each time.
10. Hence the number of permutations of n objects taken r at a
time are : nP = n(n-1) (n-r+1) In particular if all n items are to
be permutted then: nP = n(n-1)(n-{n-2}+1)(n-{n-1}+1)(n-n+1) nP =
n(n-1) 3.2.1 Consider n=10 (n-n+1) =(10-10+1) = 1 (n-{n-1}+1)
=(10-{10-1}+1) = 2 (n-{n-2}+1) =(10-{10-2}+1) = 3 And so on.
11. From previous slide nP = n(n-1) (n-r+1) For r=n for last
term nP = n(n-1)(n-{n-2}+1)(n-{n-1}+1)(n-n+1) nP= n(n-1) 3.2.1 nP=
n! (For the repeting permutation) (! = factorial)
12. Now for the non repeating permutation multiplying and
dividing the expression for nP by (n-r)(n-r-1)3.2.1 : nP = n(n-1)
(n-r+1) (n-r)(n-r-1)3.2.1 (n-r)(n-r-1)3.2.1 nP = n! (For non
repeating permutation) (n-r)!
13. nP= n! (For the repeating permutation) nP = n! (For non
repeating permutation) (n-r)!
14. DECK OF 52 CARDS 13 OF EACH SUIT
15. FOR EXAMPLE : During the construction of a mosque a builder
comes for asking the arab of Dubai that where do you want these 7
doors to be built and in what order .The Arab thinks but gets
confused and asks that if you answer my question I will give you 1
lakh dollars.Builder says yeah ask . So arab says how many total
ways are there that I can arrange these 7 doors distinctly ?
16. Meeting the confused Arab
17. SUPPOSE THAT YOU GUYS ARE THE BUILDER WHO HAS GOT THE
OPPURTUNITY TO EARN 1 LAKH DOLLARS FROM ARAB WHAT WILL BE YOUR
ANSWER ???
18. Solution: Total doors of mosque = n =7 Arrangements of
doors = r =7 For non repeating permutations: nP = n! (n-r)! nP = 7!
= 5040 ways in which arrangements can be done (7-7)!
19. Always do something different because history is made by
those who dont follow rules .. Bring the change ,create new
standards.
20. 111 I HOPE YOU HAD SOME FUN TIME WITH ME LIKE A ROLLER
COASTER? THANKS Slanear Productions
