IIT JEE , AIEEE Forum - Mathematics , Algebra

taruntanuj007

GUYS AND GIRLS

DO TELL me some book where i can find formulae for rearrangement and de arrangement etc.etc. and the formulae for the number of onto or into functions given with a specific domain

eg

How many onto/into functions can be formed with the following configuration

F(x) {a,b,c} --> G(x) { d,e,f,g }

Experts plz help!!!

konichiwa2x

regarding de-arrangements, its there in almost every good book. try asit das gupta or any fiitjee package(rankers,classroom,pinnacle). let me know if u just need the formula.

KAB

De arrangements:

If n things are arranged in a row, the number of ways in which they can be de arranged so that no one occupies its original place is

n!(1-(1/(1!))+(1/(2!))-(1/(3!))+....+(-1)ⁿ(1/(n!)))

Eg

A person writes letters to 6 friends and addresses the corresponding envelopes.The no. of ways in which all the letters are in wrong envelopes is

=6!(1-(1/(1!))+(1/(2!))-(1/(3!))+(1/(4!))-(1/(5!))+(1/(6!))

=265 ways

The no. of one-one functions that can be defined from a finite set A into a finite set B is ^n(B)P_n(A) if n(B)>=n(A) and zero otherwise.

Eg:1)no. of 1-1 from {1,2,3} into {p,q} is zero

2)no. of 1-1 from {p,q} into {{1,2,3} is ³P₂=6

The no. of onto functions from A to B is equal to the number of ways of dividing n(A) things into n(B) groups so that no group is empty if n(A)>=n(B) and is zero otherwise.

Eg:The no. onto functions from {1,2,3} onto {p,q} is

(3!/(1!*2!))+(3!/(2!*1!))=3+3=6

In your question

no. of 1-1 is ⁴P₃=24 and no. of onto is zero because n(A)<n(B)

If you have any doubt do ask!!!!

If you want experts to help then you must post the message in Ask Expert Panel.

Cheers!!!

KAB

I think you can find these in any good book like TMH or other.

taruntanuj007

I need the formulae plz help me!!!!!

taruntanuj007

See i dont have th e book ur talking abt plz explain me the procedure u emplyed for this qs as ur method seemed quite symetrical still i want to perfectly understand it!!!

KAB

Explanation about what???
I 've given the formula for 1-1 and onto functions.

taruntanuj007

Plz explain the formula for 1-1 function i really need it!!!!

KAB

The no. of one-one functions that can be defined from a finite set A(containing n(A) elements) into a finite set B (containing n(B) elements) is ^n(B)P_n(A) if n(B)>=n(A) and zero if n(B)<n(A).

Eg:1)no. of 1-1 from {1,2,3} into {p,q} is zero because n(B)<n(A)

2)no. of 1-1 from {p,q} into {1,2,3} is ³P₂=6 (Here n(A)=2 and n(B)=3)

taruntanuj007

And for onto functions and into functrions ????

Ask & Discuss Questions with Community & Experts