Question

Let R = {a, b, c, d, e} and S = {1, 2, 3, 4}. Then number of onto functions f(x) : R → S such that f(a) ≠1 is?

• A. 240
• B. 180
• C. 204
• D. 216

Answer 1

Answer: (B)

180

Answer 2

The correct answer is (B) : 180
Total no. of onto functions
$=\frac{5!}{3!2!}\times4!$
So , when f(a) = 1
$\frac{4!}{2!2!}\times3!+4!$
$\therefore$ Required functions :
= 240 -36 -24
=180