The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

Concept:

The function f(x) is said to be one to one function if 

f(a) = f(b) ⇒ a = b,   for every a, b 

Calculations:

The function f(x) is said to be one to one function if 

f(a) = f(b) ⇒ a = b,   for every a, b 

consider the co-domain {1, 2, 3}.

'1' can be related to any of the 5 numbers.
'2' can be associated with any of the other four numbers as '1' has already been associated to one of them.
leaving us with 4 options to associate 2.

finally '3' can be associated with the remaining 3 numbers.
Hence total number of ways of doing so =5 × 4 × 3
= 60

Hence, The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is 60