A) 40
B) 51
C) 101
D) 410
E) 41
Correct Answer: E
Solution :
We have\[^{56}{{p}_{r+6}}{{:}^{54}}{{p}_{r+3}}=30800:1\] \[\Rightarrow \] \[\frac{^{56}{{p}_{r+6}}}{^{54}{{p}_{r+3}}}=\frac{30800}{1}\] \[\frac{\frac{(56)!}{(56-r-6)!}}{\frac{(54)!}{(54-r-3)!}}=30800\] \[\Rightarrow \] \[\frac{56!}{54!}\times \frac{(51-r)!}{(50-r)!}=30800\] \[\Rightarrow \] \[56\times 55\times (51-r)=30800\] \[\Rightarrow \] \[51-r=10\] \[\Rightarrow \] \[r=41\]
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