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Question
A committee of 20 members sits around a table. Find the number of arrangements that have the president and the vice president together.
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Solution
A committee of 20 members sits around a table.
But, President and Vice-president sit together.
Let us consider the President and Vice-president as one unit.
They can be arranged among themselves in 2! ways.
Now, this unit with the other 18 members of the committee is to be arranged around a table, which can be done in (19 − 1)! = 18! ways.
∴ Total number of arrangements possible if President and Vice-president sit together = 18! × 2!
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