Question

You have 2 identical books on English, 3 identical books in Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf.

Answer 1

There are total of 9 books to be arranged on a shelf.
Out of these 9 books, 2 books on English, 3 books on Hindi, and 4 books on Mathematics are identical.
∴ Total number of distinct arrangements

= `(9!)/(2!3!4!)`

= `(9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(2xx3xx2xx4!)`

= 9 × 4 × 7 × 5
= 1260
∴ In 1260 distinct ways the books can be arranged on a shelf.