novels and dictionary
Probability
Level
2
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is
less than 500
at least 1000
at least 500 but less than 750
at least 750 but less than 1000
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1 solution
It is obvious that there are15 ways of picking novels and 3 ways to pick a dictionary. By the rule of product, we get 45 possibilities.
But since the position of the dictionary is settled, the order 4 novels can choose their own position, giving us 24 possibilities.(4!)
In total we have45×24=1080 which is greater than1200