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

Accepted Solution

Answer:1. 1024 functions2. 59049 functions3. 1048576 functions4. 9765625 functionsStep-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 inx * y waysi.e. xy waysIf a set has a range of n elements, there are n possible ways in each elementFirst element: n waysSecond element: n waysThird element: n waysFourth elements; n waysFifth element: n waysSixth element: n waysSeventh element: n waysEight elements; n waysNinth element: n waysTenth element: n waysAs stated above in the product rule, we have n*n*n*n*n*n*n*n*n*n*n = n^10a. n = 2 elementsNumber of Possible Functions = 2^10 = 1,024 functionsb. n = 3 elementsNumber of Possible Functions = 3^10 = 59,049 functionsc. n = 4 elementsNumber of Possible Functions = 4^10 = 1,048,576 functionsd. n = 5 elementsNumber of Possible Functions = 5^10 = 9,765,625 functions