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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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?

Similar Questions

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

If ${}^nC_{r-1}=330$,${}^nC_r=462$,and ${}^nC_{r+1}=462$,then $r$ is equal to

If ${ }^{n-3} C_r + B \cdot { }^{n-3} C_{r-1} + B^{\prime} \cdot { }^{n-3} C_{r-2} + { }^{n-3} C_{r-3} = { }^n C_r$ holds for all $n \geq r \geq 3$,then $(B, B^{\prime}) = $.

If $\binom{15}{3r} = \binom{15}{r+3}$,then $r = \dots$

Out of $14$ cricket players,$5$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $4$ bowlers?

Vedclass Test Series

Exam Paper Generator

Online Exam Module