A) 60
B) 84
C) 124
D) none of these
Correct Answer: C
Solution :
| [c] (i) Miss C is taken |
| [a] B included \[\Rightarrow \]A excluded \[{{\Rightarrow }^{4}}{{C}_{1}}{{\times }^{4}}{{C}_{2}}=24\] |
| [b] B excluded \[{{\Rightarrow }^{4}}{{C}_{1}}{{\times }^{5}}{{C}_{3}}=40\] |
| Miss C is not taken |
| \[\Rightarrow \]B does not come\[{{\Rightarrow }^{4}}{{C}_{2}}{{\times }^{5}}{{C}_{3}}=60\] |
| \[\Rightarrow \]Total=124 |
| Alternate method: |
| Case I: |
| Mr. B is present |
| \[\Rightarrow \]A is excluded and C included |
| Hence, the number of ways is \[^{4}{{C}_{2}}^{4}{{C}_{1}}=24\]. |
| Case II: |
| Mr. 'B' is absent |
| \[\Rightarrow \]No constraint |
| Hence, the number of ways is \[^{5}{{C}_{3}}^{5}{{C}_{2}}\]=100. |
| \[\therefore \]Total = 124. |
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