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1. A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr. X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?

Solution:
10C5 : when both are not included.
10C4 : when one of them is included.

Number of ways
= 10C5 + 10C4 + 10C4
= 672

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