5books can be arranged on a shelf in ways. 25 10 120 1

Option 3rd is correct.

Step-by-step explanation:

Given: Number of books = 5

We have to find number ways in which 5 books can be arranged on a shelf.

We have 5 places to arrange the books.

Consider,

Place 1 for that we have 5 options to place a book.

⇒ Number of ways for place 1 = 5

Now, Place 2 for that we have 4 options as 1 books is already placed on place 1.

⇒ Number of ways for place 2 = 4

Now, Place 3 for that we have 3 options as 2 books is already placed on place 1 & 2.

⇒ Number of ways for place 3 = 3

Now, Place 4 for that we have 2 options as 3 books is already placed on place 1 , 2 & 3.

⇒ Number of ways for place 4 = 2

Lastly, Place 5 for that we have 1 options as 4 books is already placed on before.

⇒ Number of ways for place 5 = 1

Total Number of ways = 5 × 4 × 3 × 2 × 1 = 120

Therefore, Option 3rd is correct.