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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