How many different functions are there from a set with 10 elements to sets with the following numbers of elements? a) 2 b) 3c) 4d) 5

1. 1024 functions

2. 59049 functions

3. 1048576 functions

4. 9765625 functions

Step-by-step explanation:

Denote two events with A and B, product rule states that if event A can occur in x number of ways and event B can occur in y number of ways, the two events (A and B) can occur in sequence in

x * y ways

i.e. xy ways

If a set has a range of n elements, there are n possible ways in each element

First element: n ways

Second element: n ways

Third element: n ways

Fourth elements; n ways

Fifth element: n ways

Sixth element: n ways

Seventh element: n ways

Eight elements; n ways

Ninth element: n ways

Tenth element: n ways

As stated above in the product rule, we have n*n*n*n*n*n*n*n*n*n*n = n^10

a. n = 2 elements

Number of Possible Functions = 2^10 = 1,024 functions

b. n = 3 elements

Number of Possible Functions = 3^10 = 59,049 functions

c. n = 4 elements

Number of Possible Functions = 4^10 = 1,048,576 functions

d. n = 5 elements

Number of Possible Functions = 5^10 = 9,765,625 functions