FunctionMedium
Question
The number of functions $f:\{ 1,2,3,4\} \rightarrow \{ a,b,c\}$, which are not onto, is :
Options
A.48
B.45
C.51
D.35
Solution
Sol. [Key Concept: Not-onto $=$ total $-$ onto ${= 3}^{4} -$ (number of surjections onto 3).]
No. of into function
$${= \ ^{3}C_{1}2^{4} - \ ^{3}C_{2}1 + 0 }{= 3 \times 16 - 3 \times 1 }{= 45 }$$
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