There are five different routes that a commuter can take from her home to the office. In how many ways can she make a round trip if she uses a different route coming than going?


  1. Answer: 120 ways
    Step-by-step explanation:
    Let’s label the routes a, b, c, d, and e. The goal is to come up with as many unique permutations as possible.
    1 route: a=1.               one factorial (1!) =1*1=1
    2 routes: ab, ba=2.      2!=1*2=2
    3 routes: abc, acb, bac, bca, cab, cba=6.      3!=1*2*3=6
    4 routes: 4!=1*2*3*4=24
    5 routes: 5!=1*2*3*4*5=120 ways


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