IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

hermionie

How to find the number of into and onto functions in any given relation?

eg A - ( a,b,c,d,e,f) B - (1,2,3,4)

magiclko

se this article,it will help u as here its explained

still any problem, do knock back

monur3

see there is a direct formula for this

1)no of functions from A to B= n^m (n=n(B) and m=n(A))

2)no of one one functions from A to B = ⁿC_m*m! , if n>-m

0 , if n<m

3)no of onto functions from A to B = _{[r=1 ]}

^{[n ]} (-1)^n-r ⁿC_rr^{m ,if mn}

0 , m<n

4)no of bijections = n! if m=n

0 if m is no equal to n

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