Before P and Q there are 10 intermediate stations . The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive
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Consider the illustration: _ x _ x _ x _ x _ x _ x _
where the x's represent stations for which the train didn't halt. To make sure no two halting stations are consecutive, we only choose 4 of the 7 underscores ( _ ), C(7,4) = 35.