Question

find the number of ways of selecting 3 books from 8 different;"geography" books such that a particular book is not included​

Answer 1

Answer:

We need to select 6 books by selecting any number of books of a single subject (no. of books of any subject is more than the number of books we need). There are 4 subjects.

This is equivalent to distributing 6 sweets among 4 boys.

This can be done in  

6+4−1

C  

4−1

​

=  

9

C  

3

​

=84 ways.

Hence, (B) is correct.

Step-by-step explanation:

Answer 2

Given: Total number of books = 8

Number of books to be selected = 3

To find: The number of ways of selecting the books from such that a particular book is not included​

Solution: In mathematics, combination is the selection of items from a set that has distinct members, such that the order of selection does not matter.

The formula of combination is nCr = n!/(n - r)!r!.

Since we are not selecting a particular book, the number of books to be selected from decreases by 1, which becomes 7 now.

Hence, the number of ways of selecting 3 books from 8 different geography books such that a particular book is not included​

= ⁷C₃

= 7!/(7 - 3)!3!

= 7!/(4! × 3!)

= (7 × 6 × 5)/6

= 7 × 5

= 35.

Answer: 35