Eight persons are to be transported from city | vedclass

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Question

(B) To transport $8$ persons in $3$ cars with a maximum capacity of $3$ persons each,the distribution of persons in the cars must be $(3, 3, 2)$.First

Vedclass · Accepted Answer

$1680$

Vedclass · Answer

(B) To transport $8$ persons in $3$ cars with a maximum capacity of $3$ persons each,the distribution of persons in the cars must be $(3, 3, 2)$.First,we divide the $8$ persons into groups of $3, 3,$ and $2$:$	ext{Number of ways to group} = \frac{8!}{3!3!2!} 	imes \frac{1}{2!}$Since the cars are of different makes,the order of the groups matters,so we multiply by $3!$:$	ext{Total ways} = \left( \frac{8!}{3!3!2! 	imes 2!} ight) 	imes 3!$$= \frac{40320}{6 	imes 6 	imes 2 	imes 2} 	imes 6$$= \frac{40320}{144} 	imes 6 = 280 	imes 6 = 1680$.

Eight persons are to be transported from city $A$ to city $B$ in three cars of different makes. If each car can accommodate at most three persons,then the number of ways,in which they can be transported,is $...........$.

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