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

Question

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

Infinity Learn · Accepted Answer

Four novels can be selected from $$6$$ novels in  $$6C4$$ ways. One dictionary can be selected from $$3$$ dictionaries in  $$3C1$$ ways.As the dictionary selected is fixed in the middle, the remaining $$4$$ novels can be arranged in $$4$$! ways.∴ The required number of ways of arrangement $$=6C4$$×$$3C1$$×$$4$$!$$=1080$$

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

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