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

In the subject of probability and statistics, there are two type of possible arrangements: combination and permutation. Combination is a way of arranging things wherein order does not matter. Hence, repetition can occur. In permutation, there is no repetition. This problem is therefore a combination problem. The equation is n!/r!(n-r)!, where n is the total number of items and r is the number of items you select in a group. In this case, n=5 and r=3. The term '!' is factorial. For example, when the term is 5!, that simply means 5*4*3*2*1.

Following the formula

5!/3!(5-3)! = 10

Therefore, there are 10 different ways.