Question

Eight people wait in a row for the bus, in how many ways can they be formed if two of them refuse to be together, one behind the other?

a) 4320

b) 36000

c) 30240

d) 3600

Answer 1

Number of ways in which 8 people can stand in the queue = 8! = 40320        ....................(A)

Now we find the number of ways in which the 2 people can be together

The 2 persons can be close to each other in 2 ways = 1 behind or ahead of the other ..............(B)

Now if we consider the 2 persons as 1 "group" then this group alongwith the remaining 6 persons can be arranged in 7! = 5040 ways ...............(C)

Total number of ways in which the 2 people can be together = (B) * (C) = 2*5040 = 10080

Thus, the number of ways formed by the 8 people in which the 2 people are not together

= (A) - 10080

= 40320 - 10080

= 30240

Answer :

c)       30240

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