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Question
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
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Solution
From a committee of 8 persons, a chairman and a vice chairman are to be chosen in such a way that one person cannot hold more than one position.
Here, the number of ways of choosing a chairman and a vice chairman is the permutation of 8 different objects taken 2 at a time.
Thus, required number of ways =
8P2 = `(8!)/((8 - 2)!)`
=`(8!)/(6!)`
= `(8 xx 7 xx 6!)/(6!)`
= 8 x 7
= 56
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