Let R ={ a , b , c , d , e } and S ={1,2,3,4} . Total number of onto function f: R → S such that f

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1.Relation and Function

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Let $R =\{ a , b , c , d , e \}$ and $S =\{1,2,3,4\}$. Total number of onto function $f: R \rightarrow S$ such that $f(a) \neq$ 1 , is equal to $.............$.

A

$180$

B

$170$

C

$160$

D

$150$

(JEE MAIN-2023)

Solution

Total onto function

$\frac{[5}{\left\lfloor{3}\lfloor 2\right.} \times\lfloor 4=240$

Now when $f(a)=1$

$\lfloor 4+\frac{\lfloor 4}{\lfloor 2\lfloor 2} \times\lfloor 3=24+36=60$

so required $f ^{ n }=240-60=180$

Standard 12

Mathematics

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