Question

Let set ‘A’ has 7 elements and set B has 5 elements. If one function is selected from all possible defined functions from A to B then the probability that it is onto is

• A. $\frac { 7 ! \times 2 } { 3 \times 5 ^ { 6 } }$
• B. $\frac { 7 ! } { 10 \times 5 ^ { 6 } }$
• C. $\frac { 7 ! } { 5 ^ { 6 } }$
• D. $\frac { 7 ! } { 5 ^ { 7 } }$

Answer 1

Answer: (A)

$\frac { 7 ! \times 2 } { 3 \times 5 ^ { 6 } }$

Answer 2

Total number of function from A to B = n(S) = 5⁷

total number of onto functions from A to B is

n(5) = $\frac { 7 ! } { 3 ! 4 ! }$ × 5! + $\frac { 7 ! \times 20 } { 3 }$

\ P(5) = = $\frac { 7 ! \times 2 } { 3 \times 5 ^ { 6 } }$