Raoul wants to create a weekly schedule for going to the gym. He wants to go to the gym the same three days each week, and he wants there to be at least one day in between each of his visits. How many different ways can Raoul schedule his weekly gym visits?
Details and assumptions
Raoul does not want to go to the gym on Sunday, Thursday, Saturday, since it means it would be in the gym on Saturday and Sunday of the following week.
its wrong
3 is wrong..
right answer is 7
21
7 is correct...
To find the number of different ways Raoul can schedule his weekly gym visits, we can consider the possible combinations of three days from the remaining days available (Monday, Tuesday, Wednesday, Friday).
Let's break down the problem step by step:
Step 1: Determine the total number of remaining days
First, we exclude the days that Raoul doesn't want to go to the gym (Sunday, Thursday, Saturday). That leaves us with four remaining days: Monday, Tuesday, Wednesday, and Friday.
Step 2: Find the number of combinations of three days
To find the number of different ways Raoul can schedule his gym visits, we need to calculate the number of combinations of three days from the remaining four days.
The formula for calculating combinations is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of items, and r is the number of items to be chosen.
In this case, n = 4 (the number of remaining days) and r = 3 (Raoul wants to choose three days for gym visits).
Using the formula, the calculation becomes:
4C3 = 4! / (3!(4-3)!)
= 4! / (3! * 1!)
= (4 * 3!) / (3! * 1)
= 4
So, there are 4 different ways Raoul can schedule his weekly gym visits.
The four possible combinations are:
- Monday, Tuesday, Wednesday
- Monday, Tuesday, Friday
- Monday, Wednesday, Friday
- Tuesday, Wednesday, Friday