Question

The number of onto functions from the set {1, 2, ..........., 11} to set {1, 2, .... 10} is

• A. 5 × 11
• B. 10
• C. $\frac{11}{2}$
• D. 10× 11

Answer 1

Answer: (D)

Let $A=\{1,2, \ldots, 11\}$
$\therefore n(A)=11$ and $B=\{1,2, \ldots, 10\}$
$\therefore n(B)=10$
$\therefore $ Hence number of onto function
$={ }^{n(A)} C_{n(B)} \times n(B) ! \times n(B) $
$={ }^{11} C_{40} \times 10 ! \times 10$
$=(11 \times 10 !) \times 10=11 ! \times 10$