Multiple choice

A woman has 11 close friends. Number of ways in which she can invite them to dinner if two particular of them are not on speaking terms and will not attend together is

  1. $\overset { 11 }{ \underset { \quad 5 }{ C } } \quad -\overset { 9 }{ \underset { \quad 3 }{ C } } $
  2. $\overset { 9 }{ \underset { \quad 5 }{ C } } \quad -\overset { 9 }{ \underset { \quad \quad 4 }{ 2C } } $
  3. $\overset { 9 }{ \underset { \quad 4 }{ 3C } } $
  4. $\overset { 9 }{ \underset { \quad 4 }{ C } } $
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A Correct answer
AI explanation

Let the two friends who will not attend together be A and B, and let her select any 5 friends out of the 11. The total number of ways to invite 5 friends without restriction is 11C5. The number of ways where both A and B attend together is found by assuming A and B are already selected, leaving 3 guests to be chosen from the remaining 9 friends, which equals 9C3. Therefore, the number of ways she can invite them so that A and B are not together is 11C5 - 9C3.

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