Question

There are three identical books on English, 4 identical books on Hindi, 2 identical books on Mathematics. In how many distinct ways can they be arranged on a shelf?

Answer 1

Answer:

1260

Step-by-step explanation:

Hi,

Given that there are 3 Identical  Books on English

4 Identical book on Hindi and

2 identical books on Mathematics

If all these are arranged on a shelf,

Since there are 9 books in total all of these can be arranged

in 9! ways, but since 3 identical English books can be permuted

between themselves in 3! ways giving rise to same

arrangement, we need to divide by 3!,

Also  since 4 identical Hindi books can be permuted between

themselves in 4! ways giving rise to same arrangement, we

need to divide by 4!

Since 2 identical Mathematics books  can be permuted between

themselves in 2! ways giving rise to same arrangement, we

need to divide by 2!,

So, different number of arrangements are 9!/3!4!2!

= 1260

Hope, it helps !

Answer 2

Step-by-step explanation:

Given that there are 3 Identical  Books on English

4 Identical book on Hindi and

2 identical books on Mathematics

If all these are arranged on a shelf,

Since there are 9 books in total all of these can be arranged

in 9! ways, but since 3 identical English books can be permuted

between themselves in 3! ways giving rise to same

arrangement, we need to divide by 3!,

Also  since 4 identical Hindi books can be permuted between

themselves in 4! ways giving rise to same arrangement, we

need to divide by 4!

Since 2 identical Mathematics books  can be permuted between

themselves in 2! ways giving rise to same arrangement, we

need to divide by 2!,

So, different number of arrangements are 9!/3!4!2!

= 1260