Sangeeta plans a dinner party for 6 guests. O | vedclass

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Question

(B) Total ways to choose $6$ guests out of $10$ such that two specific friends (let them be $A$ and $B$) do not attend together is calculated by consi

Vedclass · Accepted Answer

$140$

Vedclass · Answer

(B) Total ways to choose $6$ guests out of $10$ such that two specific friends (let them be $A$ and $B$) do not attend together is calculated by considering the following cases:Case $1$: Neither $A$ nor $B$ is invited.We choose $6$ guests from the remaining $8$ friends: $\binom{8}{6} = \binom{8}{2} = \frac{8 	imes 7}{2 	imes 1} = 28$.Case $2$: Exactly one of $A$ or $B$ is invited.We choose $1$ friend from ${A, B}$ and $5$ friends from the remaining $8$: $\binom{2}{1} 	imes \binom{8}{5} = 2 	imes \binom{8}{3} = 2 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 2 	imes 56 = 112$.Total ways = $28 + 112 = 140$.

Sangeeta plans a dinner party for $6$ guests. Out of $10$ friends,in how many ways can she choose the guests if two specific friends cannot attend the party together?

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