In how many ways can 10 people be seated in 2 | vedclass

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(B) Let the two specific people be $P_1$ and $P_2$. Since they cannot be in the same boat,one must be in Boat $A$ and the other in Boat $B$.Boat $A$ a

Vedclass · Accepted Answer

$2 \binom{8}{4}$

Vedclass · Answer

(B) Let the two specific people be $P_1$ and $P_2$. Since they cannot be in the same boat,one must be in Boat $A$ and the other in Boat $B$.Boat $A$ already has $P_1$,so we need to choose $4$ more people from the remaining $8$ people to fill Boat $A$. This can be done in $\binom{8}{4}$ ways.Boat $B$ will then automatically contain $P_2$ and the remaining $4$ people from the $8$ people.Since the boats are distinct (or if we consider the arrangement of the two groups),the total number of ways is $\binom{8}{4} + \binom{8}{4} = 2 \binom{8}{4}$.

In how many ways can $10$ people be seated in $2$ boats such that each boat has $5$ people and two specific people do not sit in the same boat?

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