Question

In a shelf, there are 8 English, 6 Telugu books. The number of ways can 6 books be chosen if there is no restriction in the choice of books is
A. $^{18}{C_6}$
B. $^{14}{C_6}$
C. $^8{C_3}{.^6}{C_3}$
D. $^{10}{C_6}$

Answer 1

First of all we will find the total number of books that are given by adding the number of English books and Telegu books. Then we will use the concept of combination to find the number of ways in which 6 books can be chosen, that is if there are total $n$ objects and $r$ objects are to be selected, then the number of ways is $^n{C_r}$.

Complete step by step answer:

We are given that there are 8 English books and 6 Telegu books.
We will begin by finding the total number of books.
We will add the number of English and Telegu books.
So, this means there are $8 + 6 = 14$ books in the shelf.
We have to choose 6 books out of them.
Whenever we have to select some objects such that the order of the selection does not matter, we use the combination.
If there are a total of $n$ objects and $r$ objects are to be selected, then the number of ways is $^n{C_r}$.
Hence if we have to select 6 books from 14 books, this implies and $r = 6$ in the above expression.
Hence, the number of ways is $^{14}{C_6}$
Thus, option B is correct.

Note: Many students make mistakes by using permutation instead of combination in the given question. We use permutation when the order of the objects matter. But, here the order of the selection of the books does not matter. Also, the formula $^n{C_r}$ is equivalent to $\dfrac{{n!}}{{r!\left( {n - r} \right)!}}$