Question

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 A. 1 5 B. 1 550 C. 1 505 D. none of these Select the correct answer from above options

Answer 1

Correct Answer - D The total number of ways of arranging 50 books in shelf is .50P50=50! Out of 50 places, 5 places for the five-volume dictionary can be chosen in .50C5 ways. In the remaining 45 places the remaining 45 books can be arranged in .45P45=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 =.50C5×45! Hence, required probability = .50C5×45! 50! = 1 120