how many ways can five birds line up along a railing?

Question

Combinations and permutations

Answer 1

This is a permutation based problem, because order matters. Since there are 5 birds and we're trying to find the number of the ways that the 5 of them can be ordered on the railing, then this can be solved with a simple factorial.

 

5! = 5 * 4 * 3 * 2 * 1 = 120 different ways to order the five birds.

 

Explanation: For the first bird, we have 5 choices. After we choose one bird, 4 remain. So for the second position on the railing, we have 4 choices of bird. After choosing the second bird, 3 birds remain, and it continues in this fashion until there are no more birds. These numbers are multiplied together, because for every 5 first choices of bird, there are 4 remaining choices of bird (20 possible outcomes for the first two positions railing), followed by 3 remaining choices of bird (60 outcomes for the first three positions on the railing), followed by 2 remaining choices of bird (120 outcomes for the first four positions), and then one last bird, which we must choose, so it does not increase the number of outcomes (120 * 1 = 120).

 

Let me know if this explanation makes sense! I can try to elaborate if necessary.