A lady gives a dinner party to six quests. 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 (a) 112 (b) 140
(c) 164 (d) None of these

• total no of ways to select 6 frm 10=10C6=210
  total ways of selecting the 2 always = 2C2*8C4=70
  so req no ways = 210 - 70 = 140
• 9 years agoHelpfull: Yes(44) No(2)
• Can invite only one of those two= Invite all - ways in which can invite hose two together;
  => 10C6 ( inviting ut of 10 ) - 8C4 ( ways in which two will always come together )
  => 140
• 9 years agoHelpfull: Yes(11) No(1)
• Their is a concept for these type of problem is:-
  if it is mention their some particular thing should not be together for that
  we applied one formula -> ncr - n-kcr-k where k is particular things
  so, 10c6 - 8c4 will be ans.
• 9 years agoHelpfull: Yes(7) No(0)
• Answer should be 140.
  we have two cases either she invite one of those two friends or does not invite any of them.
  1-2*8c5
  +
  2-8c6
  =140
• 9 years agoHelpfull: Yes(2) No(0)
• Its a simple Problem, We can solve it into 2 ways
  Let 8 and P, Q, these are 10 friends
  P attend Q not attend= 8C5=56
  Q attend Q not attend=8C5=56
  Neither P attend not nor Q attend=8C6=28
  Total no. ways= 56+56+28=140
  Another Method
  Total no. ways - If P and Q both attend = 10C6-8C4 =210-70=140
• 8 years agoHelpfull: Yes(2) No(0)
• 9c6+9c6=168
• 9 years agoHelpfull: Yes(1) No(7)
• choosing 6 quest form 10 person can be done in 10C6 ways
  choosing 6 quest form 10 person such that two person can come together can be done in 2*9c6 ways
  choosing 6 quest from 10 person such that no two person can come together can be done in 10c6-2*9c6
  so ans should be none of these
• 9 years agoHelpfull: Yes(0) No(2)
• answer is c=164
  
• 9 years agoHelpfull: Yes(0) No(3)
• two cases either she invite one of those two friends or does not invite any of them.
  9C6+8C6=112
• 9 years agoHelpfull: Yes(0) No(5)
• No of friends invited= 6 AND a and b be the 2 guys who will not attend the party together.
  Then the number of ways of selecting / inviting friends = (10-2)C6 * 2C0 + (10-2)C5 * 2C1 = 140
• 9 years agoHelpfull: Yes(0) No(0)
• 112. is the ans
• 9 years agoHelpfull: Yes(0) No(3)
• ans :- option d
  because my ans is 168
  reject 1 friend now we have 9 friends
  we have to select 6 from 9 friends i.e 9c6
  and rejection of one friend is done in 2 ways
  so total no of ways=2*9c6=168
  
• 9 years agoHelpfull: Yes(0) No(3)
• answer is B
• 8 years agoHelpfull: Yes(0) No(0)
• No. of friends to be invited=6
  Let x,y be the friends who are not to attend the party together.
  Therefore, Either none of x,y or one of x,y attend the party
  Therefore,no of ways to inviting friends=
  (10-2C6 * 2C0 ) +(10-2C5 * 2C0)
  =28*1+56*2
  =140
• 8 years agoHelpfull: Yes(0) No(0)
• a)112
  let us take two friend we are not taking together are: A and B
  case1: taking A , not taking B.... and selecting other 5 friend 8C5
  case2: taking B, not taking A. nd and selecting other 5 friend . 8C5
  answer: case1+case2= 120
• 7 years agoHelpfull: Yes(0) No(0)