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  • From 6 different novels and 3 different dictionaries, 4 novels and I dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number o

From 6 different novels and 3 different dictionaries, 4 novels and I dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is

Option: 1

at least 750 but less than 1000


Option: 2

at least 1000


Option: 3

 less than 500


Option: 4

at least 500 but less than 750


Answers (1)

best_answer

We can choose 4 novels out of 6 in \mathrm{{ }^{6} C_{4}} ways and 1 dictionary out of 3 in \mathrm{3 C_{1}} ways. We can arrange 4 novels and 1 dictionary in the middle in 4 ! ways. Thus, required number of ways

\mathrm{=\left({ }^{6} C_{4}\right)\left({ }^{3} C_{1}\right)(4 !)=1080>1000}

Posted by

Irshad Anwar

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