Question:

Let $R=\{a,b,c,d,e\}$ and $S=\{1,2,3,4\}$. Total number of onto functions $f:R\to S$ such that $f(a)\neq1$ is equal to ________.

Step-by-Step Solution

Key Concept: Total onto functions $R\to S$ minus those with $f(a)=1$. Use inclusion-exclusion for onto functions from 5-element to 4-element set.

$240-60=180$.

Correct Answer: 180