# If $A=\left \{ a,b,c \right \}\: \: and\: \: B=\left \{ \left ( 1,2,3,4 \right ) \right \}$ then the no. of elements in the set $C=\left \{ f:A\rightarrow B|2\in f(A)\, \right \}$ and $f$ is not one-one is............ Option: 1 15 Option: 2 16 Option: 3 18 Option: 4 19

Let say a has image 2 then b and c both should have single image 1/3/4, Total selection will be 3

If a has option to choose 1/3/5 then b and c have only one option 2 Total selection will be 3

Here if we rearrange a,b c it has 3 option so total number of ways is 3 X ( 3 + 3) = 18

Now if a b c has one option as 2

Total selection is 18 +1 = 19.

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