Consider 36 students to be seated such that each row has same number of students as others . If atleast 3 students are to be seated per row and atleast 2 rows have to be there. How many arrangements are possible?
Answers
Answer:
6 arrangements are possible
Step-by-step explanation:
According to question, 3 condition are to be satisfied and they are :
( 1 ) The number of students per row has to be at least 3.
( 2 ) Number of row has to be at least 2.
( 3 ) Equal number of students has to be seated in a row.
The following arrangements will satisfy all 3 conditions.
1: 3 * 12
3 students in a row = 12 rows.
2: 4*9
4 students in a row = 9 rows.
3: 6*6
6 students in a row = 6 rows.
4: 9*4
9 students in a row = 4 rows.
5: 12*3
12 students in a row = 3 rows
6: 18*2
18 students in a row = 2 rows
Now,
Factors of 36 – 1, 2, 3, 4, 6, 9, 12 , 18 and 36.
Aa condition 1 says number of students in each row must be at least 3 and the number of rows is at least 2.
Both the conditions are satisfied for the following factors : 3, 4, 6, 9, 12, 18
So,
Number if arrangements is 6
Hence,
6 arrangements are possible