Problema Solution
Daily Routine
Aji has an argument with his daughter. She says, "You do the same darn thing every day" Agi does go fishing every day, but contend that every day is different because he does things in a different order each day. Before he leaves shore in his rowboat, he gets fresh bait, checks the weather, and adjusts his seat cushion. Out in the water, he eats his fruit, puts the meat on his sandwich, drinks his apple juice, and eats his sandwich. Back at shore, after trying his boat to the dock, he takes the fishing pole in his right hand and the ice chest in his left hand. Then he finally heads back home to have the same argument with his daughter. For how many days could Aji do things in a different order before he has to repeat the order of some prior day? Is there any easy way he could double the number of days in his cycle?
Answer provided by our tutors
- Before he leaves shore in his rowboat the following events happen: he gets fresh bait, checks the weather, and adjusts his seat cushion
these are 3 independent events for which the order is not important thus he can do them in 3! = 6 different orders.
- Out in the water: he eats his fruit, puts the meat on his sandwich, drinks his apple juice, and eats his sandwich
we have 4 different events in which is important that he first must put the meat on the sandwich and then eat the sandwich thus 2 of the events are not independent - the total number of orders of this events is 12
- Back at shore, after trying his boat to the dock, he takes the fishing pole in his right hand and the ice chest in his left hand
these are 2 independent events and they can be arranged in 2! = 2 ways
the total number of different orders will be 6*12*2 = 144
Aji can do things in a different order for 144 days.