Question

A teacher has to arrange 56 students in different row . Find out how many ways he can arrange students with the same number in each row​

Answer 1

Prime factories 40=2×2÷2×5.

40 has factors 1 2 4 5 8 10 20 40 = 8 factors giving value of r=rows. Number of columns =c=(40/r).

Other method ;

Distribute these 4 prime factors as rows × columns to form a rectangle as

2×20 20×2 4×10 10×4 8×5 5×8

Or Total 6 possible pairs of values as above assuming number of rows and columns is >=2.

However, if it is possible that r or c=1 allowed, then 2 more pairs of values 1,40 & 40,1 thus taking total possible values to (6+2)=8 pairs of values.

Answer 2

Step-by-step explanation:

Given that a teacher has to arrange 56 students in different row. If there is only 1 row then there are 56 columns while two rows will have 28 columns.

So, it's Frist possible arrangement is 2 × 28. As we can't put three students in a row so it's second possible arrangement will be 4 × 14 means four students in each row with 14 rows.

Similarly other arrangements are

7 × 8, 8 × 7, 14 × 4 and 28 × 2

So, the possible arrangements of the students with the same number in each row:

2 × 28

4 × 14

7 × 8

8 × 7

14 × 4

28 × 2