Statistics And Probability Question 231
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:
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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
