A lady gives a dinner party for 6 guests. The | vedclass

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(B) Total number of ways to select $6$ guests from $10$ friends without any restriction is $^{10}C_6 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3

Vedclass · Accepted Answer

$140$

Vedclass · Answer

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

$A$ lady gives a dinner party for $6$ guests. The number of ways in which they may be selected from among $10$ friends,if two of the friends will not attend the party together,is:

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