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In how many ways can a daily revision routine of at least one chapter of each subject be made from 12 Mathematics chapters, 5 Science chapters, 6 History chapters and 11 English chapters?
Option: 1
$2^3\left(2^2+1\right)\left(2^3+3\right)$

Option: 2
$2^3\left(2^2+1\right)\left(2^2+3\right) 3^2$

Option: 3
$\left(2^2+1\right)\left(2^3+3\right) 3^2$

Option: 4
$2^3\left(2^2+1\right)\left(2^3+3\right) 3^2$

Answers (1)

best_answer

Note the following:

The formula for the combination for the selection of the $\mathrm{x}$ items from the $\mathrm{y}$ different items is $\mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}$

The combination for the selection of the none or more items from the $\mathrm{n}$ identical items is $\mathrm{=n+1}$

From the available data, the following is evident.

The combination for the selection of the one or more Mathematics chapters is $=12$
The combination for the selection of the one or more Science chapters is $=5$
The combination for the selection of the one or more History chapters is $=6$
The combination for the selection of the one or more English chapters is $=11$

Therefore, the required combination for selection of at least one chapter of each subject is

$=12\times5\times6\times11$

$=2^{2}\times3\times5\times2\times3\times11$

$=2^{2}\left ( 2^{2}+1 \right )\left ( 2^{3} +3\right )3^{2}$

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shivangi.bhatnagar

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