On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?

a)
3846

b)
2880

c)
900

d)
1200

Correct answer is option 'B'. Can you explain this answer?

Question

On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?

a)
3846
b)
2880
c)
900
d)
1200

Correct answer is option 'B'. Can you explain this answer?

Answer

First, we consider each subject as one group. So, we have 3 groups to arrange. The number of ways to arrange these groups is 3!.
Within each group, the books can also be arranged. The number of ways to arrange 2 Geology books is 2!, the number of ways to arrange 2 Sociology books is 2!, and the number of ways to arrange 5 Economics books is 5!.
So the total number of ways to arrange the books is 3! * 2! * 2! * 5! = 6 * 2 * 2 * 120 = 2880 ways.

Answer

There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways.
Further, in each category (subject), books are to be arranged in different order, we get,
Required number of ways:

3! * [2! * 2! * 5!] = 2880

Answer

First, we consider each subject as one group. So, we have 3 groups to arrange. The number of ways to arrange these groups is 3!.
Within each group, the books can also be arranged. The number of ways to arrange 2 Geology books is 2!, the number of ways to arrange 2 Sociology books is 2!, and the number of ways to arrange 5 Economics books is 5!.
So the total number of ways to arrange the books is 3! * 2! * 2! * 5! = 6 * 2 * 2 * 120 = 2880 ways.

Answer

There are books of 3 subjects (Geology, Sociology and Economics), hence they can be arranged in 3! (3 * 2 * 1) = 6 ways.
Further, in each category (subject), books are to be arranged in different order, we get,
Required number of ways:

3! * [2! * 2! * 5!] = 2880

Answer

To find the number of ways the books can be arranged, we need to consider the different arrangements of each subject and then multiply them together.

Let's start with the books of Geology. Since there are 2 books of Geology, they can be arranged among themselves in 2! = 2 ways.

Similarly, the 2 books of Sociology can be arranged among themselves in 2! = 2 ways.

And the 5 books of Economics can be arranged among themselves in 5! = 120 ways.

Now, we need to consider the arrangement of the subjects themselves. Since there are 3 different subjects (Geology, Sociology, Economics), they can be arranged among themselves in 3! = 6 ways.

To get the total number of arrangements, we multiply all the individual arrangements together:

Total arrangements = (Number of arrangements of Geology) * (Number of arrangements of Sociology) * (Number of arrangements of Economics) * (Number of arrangements of subjects themselves)

Total arrangements = 2 * 2 * 120 * 6 = 2880

Therefore, the correct answer is option b) 2880.

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