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