CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the number of ways in which a selection of $$5$$ books can be done out of $$3$$ physics, $$3$$ chemistry and $$3$$ mathematics books by taking at least one book of each subject, books of same subject being different.


Solution

$$\begin{array}{l} Total\, number\, of\, ways\, =books\, can\, be\, taken\, in\, group\, of\, \left( { 1,3,1 } \right) +In\, group\, of\, \left( { 1,2,2 } \right) \, from\, maths\, ,\, physics\, and\, chemistry. \\ =\dfrac { { 3! } }{ { 2! } } \left( { ^{ 3 }{ C_{ 1 } }{ \times ^{ 3 } }{ C_{ 3 } }{ \times ^{ 3 } }{ C_{ 1 } } } \right) +\dfrac { { 3! } }{ { 2! } } \left( { ^{ 3 }{ C_{ 1 } }{ \times ^{ 3 } }{ C_{ 3 } }{ \times ^{ 3 } }{ C_{ 1 } } } \right)  \\ =\dfrac { { 3\times 1\times 3\times 3\times 2 } }{ 2 } +\left( { 3\times 3\times 3 } \right) \dfrac { 6 }{ 2 }  \\ =27+81 \\ =108 \end{array}$$
Which, is the required answer.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image