Question

If we put 5 math, 6 biology, 8 engineering, and 3 physics books on a bookshelf at random, what is the probability that all the math books are together?

Answer 1

Answer:
`(3)/(4389)`

Explanation:

Given : Number of math books = 5

Total number of books = 5+6+8+3=22

Number of books except math = 17

Number of ways to arrange 22 books in bookshelf =
`22!`

When all math books are together , then we count whole set as one

Now, the number of objects in bookshelf = 17+1=18

Number of ways to arrange books such that all math books are together =
`18!5!`

Now, the probability that all the math books are together :-

`(5!18!)/(22!)=(3)/(4389)`

Hence, the probability that all the math books are together
`=(3)/(4389)`