A) \[\frac{1}{5}\]
B) \[\frac{1}{{{5}^{50}}}\]
C) \[\frac{1}{{{50}^{5}}}\]
D) None of these
Correct Answer: D
Solution :
[d] The number of ways of arranging 50 books \[{{=}^{50}}{{P}_{50}}=50!\]. The number of ways of choosing places for the vive volume dictionary is \[^{50}{{C}_{5}}\] and the number of ways of arranging the remaining 45 books \[{{=}^{45}}{{P}_{45}}=(45)!\] Thus the number of favourable ways is \[{{(}^{50}}{{C}_{5}})(45!).\] Hence the probability of he required event \[=\frac{\left( ^{50}{{C}_{5}} \right)(45!)}{50!}=\left( \frac{50!}{5!45!} \right)\left( \frac{45!}{50!} \right)=\frac{1}{5!}=\frac{1}{120}\]
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