in how many different ways can five elements be selected in

in how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?

Solution

You can split this up into five simpler tasks.
1. Choose an element to be \"the first element\".This can be done in 3ways
2. Choose an element to be \"the second element\"..This can be done in 3ways
3. Choose an element to be \"the third element\"..This can be done in 3ways
4. Choose an element to be \"the fourth element\"..This can be done in 3ways
5. Choose an element to be \"the fifth element\"..This can be done in 3ways

Each of these tasks can be completed in 3 ways, because there are 3 elements to choose from five elements

. So the total number of ways of selecting five elements is

3*3*3*3*3 = 3^5 = 243.