Dont be consecutive

Probability Level pending

20 persons are in a row and John wants to pick 7 out of them.In how many ways can John select them such that at least one person finds the person next to him (in the row) is also selected. If K is the number of ways, give your answer as greatest integer less than K 1 0 4 \frac{K}{10^4}

7 8 6 9

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1 solution

Benny Joseph
Feb 12, 2018

No. of ways = total no. of ways of selecting 7 people - (No. of ways in which no two people are consecutive) = ( n r ) \binom{n}{r} - ( n r + 1 r ) \binom{n-r+1}{r} ; K = ( 20 7 ) \binom{20}{7} - ( 14 7 ) \binom{14}{7} ; K 1 0 4 \frac{K}{10^4} = 7.4088

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