Probability Question 62
Question: There are 5 volumes of Mathematics among 25 books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is
Options:
A) $ \frac{1}{5!} $
B) $ \frac{50!}{55!} $
C) $ \frac{1}{50^{5}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Five places for 5 volumes of Mathematics from 25 places of books can be select in $ {}^{25}C_5 $ ways.
In these places, we are not to permute the 5 volumes since order of these 5 volumes is fixed i.e., $ v_1,v_2,v_3,v_4,v_5. $
Remaining 20 books can be arranged in $ 20! $ ways.
$ \therefore $ Favourable ways $ ={}^{25}C_5.20!=\frac{25!.20!}{5!20!}=\frac{25!}{5!} $ Also total number of ways $ =25! $
$ \therefore $ Probability $ =\frac{25!}{5!25!}=\frac{1}{5!} $ .
BETA
