A certain virus afflicted the families in fou adjacent house

A certain virus afflicted the families in fou\' adjacent houses in a row of 12 houses. If houses were randomly chosen from a row of 12 houses, what is the probability that the \"\'our houses would be adjacent? (Round your answer to three decimal places.)

Solution

No of ways of choosing 4 houses from 12 = ¹²C₄

consider 4 adjacent houses to be one single packet (8 houses + 1 packet = 9)

No of ways of choosing 4 adjacent houses = ⁹C₄

==> Probability that four houses would be adjacent = (⁹C₄)/(¹²C₄) ; ⁿC_r = n!/[ (n - r)! r! ]

==> (126)/(495)

==> 14/55

==> 0.255

Hence Probability that four houses would be adjacent = 0.255