Question

There are 5 books on mathematics and 6 books on physics in a bookshop. In how many ways can a student buy a mathematics book and a physics book?

Answer 1

Hint: Hint: This question is based on the concept of simple permutations and combinations. To be more precise, this question is a typical example of combinations. So simply make use of the combination formula as given by equation 1.
Formula Used:
${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$ --(1)
Where n = total number of cases possible, r = selection out of n cases.

Complete step-by-step answer:
Steps in this question begin with the understanding of the requirement asked 1 in the question.
Step1: Write the information given in the question which is
Total books of mathematics = 5
Total books of physics= 6
Step 2: Question just asks about how a mathematics book and a physics book is selected. Remember to choose only one book and not more than that.
Step 3: Now we will perform the selection of one book each from mathematics and physics.
To select one book from Mathematics we can write it as ${}^5{C_1}$
Similarly, to select one physics book we can write it as \[{}^6{C_1}\]
Step 4: Now to write down the final step we need to combine (by multiplying) both the selection given in step3. Therefore, we will get = \[{}^6{C_1}\]×${}^5{C_1}$
Final answer: The number of ways by which a math’s and a physics book is selected together is \[{}^6{C_1}\]×${}^5{C_1}$ which is equal to ${}^{30}{C_1}$=$30$

Note: The thing that needs to be kept in mind is to just understand the concept of selection and arrangement before attempting such a question. Order of selection is a factor in Permutations. Order does not matter in Combinations.