Probability Question 384
Question: There is a five-volume dictionary among 50 books arranged on a shelf in random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right is:
Options:
A) $ \frac{1}{5} $
B) $ \frac{1}{5^{50}} $
C) $ \frac{1}{50^{5}} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
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{( ^{50}C_5 )(45!)}{50!}=( \frac{50!}{5!45!} )( \frac{45!}{50!} )=\frac{1}{5!}=\frac{1}{120} $
BETA
