BITSAT2010MathematicsFunctionsActual
Let (E= 1,2,3,4 ) and (F= 1,2 ). Then the number of onto functions from ( E ) to ( F ) is
Options
- A14
- B16
- C12
- D8
Correct answer
A. 14
Step-by-step solution
If set (A ) has (m ) elements and set (B ) has ( n ) elements then number of onto functions from (A ) to (B ) is ( _ r=1 ^n(-1)^ n-r ^n C_r r^m where 1 n m ) Here (E= 1,2,3,4 , F= 1,2 ) (m=4, n=2 ) ( ) No. of onto functions from ( E ) to ( F ) ( aligned & = _ r=1 ^2(-1)^ 2-r ~2 C_r(r)^4 & =(-1)^2 C₁+ ^2 C₂(2)^4=-2+16=14 aligned )