A lady gives a dinner party for six guests. T | vedclass

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(B) Total friends available = $10$. We need to select $6$ guests.Let the two friends who will not attend together be $A$ and $B$.Total ways to select

Vedclass · Accepted Answer

$140$

Vedclass · Answer

(B) Total friends available = $10$. We need to select $6$ guests.Let the two friends who will not attend together be $A$ and $B$.Total ways to select $6$ guests from $10$ without any restriction = $^{10}C_6 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$.Ways in which both $A$ and $B$ are selected = We need to select $4$ more guests from the remaining $8$ friends = $^8C_4 = \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 70$.The number of ways in which $A$ and $B$ do not attend together = (Total ways) - (Ways where both $A$ and $B$ are selected) = $210 - 70 = 140$.

$A$ lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends,if two of the friends will not attend the party together is

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