Math Problem of the Week - Algebra and Up - Mar. 6, 2022 to Mar. 12, 2022

Algebra and Up: 

Question: Five people sit down for a fancy dinner. Each of their napkins is folded into a different origami animal - a swan, a frog, a rabbit, a fish, a pig, or a turtle. The person at the head of the table always gets the rabbit. How many different ways can the napkins be arranged around the table? 

Answer: 120

Solution: Because the rabbit must be at the head of the table, we only need to find the number of possible animals for the other 4 place settings. There are 5 options for the first place setting's animal, folllowed by 4 remaining options for the next place setting, 3 for the thrid place setting, and 2 for the fourth. To find the number of possible combinations, we multiply the number of possibilities for each place setting together. So, there are 5 x 4 x 3 x 2 = 120 possible arrangements.