Question:

A boy has $3$ library tickets and $8$ books of his interest in the library. Of these $8$, he does not want to borrow Mathematics unless Mathematics is also borrowed. In how many ways can he choose the three books to be borrowed?

Updated On: Jul 5, 2022
  • $40$
  • $45$
  • $42$
  • $41$
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The Correct Option is D

Solution and Explanation

Let us make the following cases : Boy borrows Mathematics Part II, then he borrows Mathematics Part I also. So, the number of possible choices is $^{6}C_{1} = 6$. Boy does not borrow Mathematics Part II, then the number of possible choices is $^{7}C_{3} = 35$. Hence, the total number of possible choices is $= 35 + 6 = 41$.
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Notes on permutations and combinations

Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.