# Entrance exams

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Elections are to be scheduled on any 7 days in April and May.In how many ways can the seven days be chosen such that elections are not scheduled on 2 consecutive days?

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Elections are to take place in 7 days in April and May, so our job is to choose those 7 days such that the elections are not scheduled on 2 consecutive days.

Total number of days are = 30+31= 61 days.

Hence we have to choose 7 days i.e., d1,d2,d3,d4,d5,d6,d7 from the set {1,2,3,4,5,…..,61}.

Since these di’s are to be non consecutive, that means we can take di’s of the form di=ai+(i-1) for all i=1(1)7. Now our work reduces to choosing ai’s which automatically makes the di’s non-consecutive.

d7<=61 i.e., a7+6<=61 i.e., a7<=55, i.e., to choose a1<a2<a3<a4<…<a7 from the set {1,2,3,…..,55}, i.e., Total number ways in which the task can be done = 55C7 ways which is our desired answer.