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LET SET A (1,2,3,4,5) & B(1,2,3) THEN a) NUMBER OF ONTO FUNCTIONS FROM A TO B ? b) NUMBER OF ONE ONE FUNCTIONS FROM A TO A SUCH THAT F(i) ≠ i, i € A c) NUMBER OF INTO FUNCTIONS FROM A TO B ? PLZ REPLY

LET SET A (1,2,3,4,5) &  B(1,2,3) THEN 


a) NUMBER OF ONTO FUNCTIONS FROM A TO B ?


b) NUMBER OF ONE ONE FUNCTIONS FROM A TO A SUCH THAT F(i) ≠ i, i € A


c) NUMBER OF INTO FUNCTIONS FROM A TO B ? 


PLZ REPLY 

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

I will give u very short trick:

In general no of onto functions from A to B containing m and n elements respectively is



\sum _{r=1}^{n} (-1)^{n-r} nC_r.r^m

 

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Sagar Singh

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