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  • There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of: a)One book of each subject i)3968

There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of: 

\begin{array}{|l|l|l|l|} \hline \text { C }_{\mathbf{1}} & & \mathbf{C}_{2} & \\ \hline \text { (a) } & \begin{array}{l} \text { One book of each } \\ \text { subject: } \end{array} & \text { (i) } & 3968 \\ \hline \text { (b) } & \begin{array}{l} \text { At least one book } \\ \text { of each subject: } \end{array} & \text { (ii) } & 60 \\ \hline \text { (c) } & \begin{array}{l} \text { At least one book } \\ \text { of English: } \end{array} & \text { (iii) } & 3255 \\ \hline \end{array}


 

Answers (1)

Number of book of mathematics=3

Number of book of physics=4 

Number of book of English=5  

 a.One book of each subject= ^3C_1*^4C_1*^5C_1=60 

 b.At least one book of each subject=\left (2^3-1 \right )\left (2^3-1 \right )\left (2^5-1 \right )=3225

 c. Adding one book of English=\left (2^5-1 \right ).2^7=3968   

 So, a-(ii), b-(iii),  c-(i)

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