There is a five –volume dictionary among 50 books arranged on a shelf in a 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. `(1)/(5)`
B. `(1)/(5^(50))`
C. `(1)/(50^(5))`
D. none of these

Answer

D

Explanation

The total number of ways of arranging 50 books in shelf is `.^(50)P_(50)=50!` Out of 50 places, 5 places for the five-volume dictionary can be chosen in `.^(50)C_(5)` ways. In the remaining 45 places the remaining 45 books can be arranged in `.^(45)P_(45)=45!` ways. In the five places five volumes of dictionary can be arranged in increasing order in one way only.
So, favourable number of ways `=.^(50)C_(5)xx45!`
Hence, required probability `=(.^(50)C_(5)xx45!)/(50!)=(1)/(120)`