a.
Tocalculate:The number of clockwise loop arrangements possible for letter A, B and C.
The number of clockwise loop arrangements possible is 2.
Given information:
It is given that three letters A, B and C.
Calculation:
Consider the given information.
It is given that three letters should be arranged in a loop.
So, there are 2! possible arrangements.
The number of clockwise loop arrangements possible for letter A, B and C is 2! Which is equal to 2.
Thus, the number of clockwise loop arrangements possible is 2.
b.
Toidentify:The number of loop arrangements possible for letter A, B, C and D.
The number of loop arrangements possible is 6.
Given information:
The given diagram is shown below:
Explanation:
Consider the given information.
It is given that four letters should be arranged in a loop.
So, there are 3! possible arrangements.
As in making a loop one point is fixed, so possible arrangements can be made with 3.
The number of loop arrangements possible for letter A, B, C and D is 3! Which is equal to 6.
Thus, the number of loop arrangements possible is 6.
c.
To identify:The expression for the number of clockwise loop arrangements for n objects.
The required expression for the number of clockwise loops is
Given information:
The given number of objects are n .
Explanation:
Consider the given information.
Follow the same procedure as mentioned in above the number of arrangements possible for n objects is
Thus, the number of possible arrangements are
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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