Chapter CSB1.1, Problem 21E

a.

To determine

Whether the whole band can be arranged in rows of 7 or not.

Answer to Problem 21E

No

Explanation of Solution

Given information:

Total number of students in band = 72.

Students need to march in row and number of students in each row should be same.

In order for whole band to be arranged in rows of 7, the total number of students should be completely divisible by 7.

Now as 72 is not divisible by 7. Therefore whole band cannot be arranged in rows of 7.

b.

To determine

The number of ways in which students can be arranged.

Answer to Problem 21E

12 ways

Explanation of Solution

Given information:

Total number of students in band = 72.

Students need to march in row and number of students in each row should be same.

To find the ways of arrangement of students in band first find factors of 72.

Factors can be found by dividing the number 72 starting from 1, 2, 3 and so on. For each full division the divider and quotient will form the factor of 72. The process should be stopped when numbers starts repeating.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

Since there are total 12 factors hence students can be arranged in 12 ways. The arrangements are as follows:

• 72 rows of 1 students
• 36 rows of 2 students.
• 24 rows of 3 students.
• 18 rows of 4 students.
• 12 rows of 6 students.
• 9 rows of 8 students.
• 8 rows of 9 students.
• 6 rows of 12 students.
• 4 rows of 18 students.
• 3 rows of 24 students.
• 2 rows of 36 students.
• 1 row of 72 students.