Question

Two books are to be selected random without replacement out of four books.then numbers of selections are

Answer 1

The number of selections is 6.

Step-by-step explanation:

We are given that two books are to be selected randomly without replacement out of four books.

Firstly, we have to decide whether we use combination or permutation to solve the above problem.

As we know that Permutation is used when the order of selection matters and on the other hand Combination is used when the order of selection doesn't matter.

So, according to our question, the order for the selection of books doesn't matter to us, that's why we will use a Combination here.

Total number of books available = 4 books

Number of books needs to be selected = 2 books

So, the numbers of selections in which this can be done =  $^{4}C_2$

                   =  $\frac{4!}{2! \times (4-2)!}$           { $\because \text{ }^{n}C_r = \frac{n!}{r!\times (n-r)!}$ }

                   =  $\frac{4!}{2! \times 2!}$

                   =  $\frac{24}{4}$  = 6

Hence, the numbers of selections are 6.