At an election meeting six speakers have to address the meeting. The President of the party is to speak before the M.L.A. of the constituency. In how many ways can this be done? In how many of these arrangements will the M.L.A. speak just after the speech of the President?

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Solution

This question is another version of above question.
Let P = President, Q = M.L.A.
6 speakers dn be arranged in $6$ ways. In these arrangements P may speak either before Q or after Q Since we want P to address before Q
$∴$ Required number is $\frac{1}{2}$ $(6!) = 360$ .
In case P and Q are to be consecutive speakers then follow string method, i.e., tie them and we are left with 5 units (P and Q being counted as one). They- can address in $5! 2! = 240$ ways.
2! corresponds to 2 arrangements of P and Q. But we want only PQ and not QP, as Q is to address just after P. Hence the required number is
$\frac{1}{2}$ $(240) = 120$ .

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