According to the given question, Scott has seven chores to complete this Saturday, and we have to find many ways can he arrange the order in which he does them.
Step 1: Understand the Problem
The problem is asking how many different ways Scott can arrange the order in which he does his 7 chores.
This is a problem of permutations, a concept in combinatorics, which is a branch of mathematics concerned with counting, arrangement, and combination.
Step 2: Identify the Concept Used
The concept used here is the factorial function, denoted by the symbol (!).
In mathematics, the factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is used to calculate the number of ways an event can occur.
Step 3: Apply the Concept to the Problem
In this case, we want to find ways to arrange 7 chores, which is represented as 7! This means we multiply all the positive integers from 7 down to 1.
Step 4: Perform the Calculation
Let’s break down the calculation:
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
- First, multiply 7 and 6 to get 42.
- Then, multiply 42 and 5 to get 210.
- Multiply 210 and 4 to get 840.
- Multiply 840 and 3 to get 2520.
- Multiply 2520 and 2 to get 5040.
- Finally, multiply 5040 and 1 to get 5040.
Step 5: Interpret the Result
The result, 5040, represents the number of different ways Scott can arrange the order in which he does his 7 chores.
This means that there are 5040 different sequences in which Scott can complete his chores.
Scott has 7 chores to complete this Saturday; the no of ways the chores can be arranged is 5040