Steel express stops at six stations
between Howrah and Jamshedpur. Five passengers board at Howrah. Each passenger
can get down at any station till Jamshedpur. The probability that all five
persons will get down at different stations is:

A.6P5/6

^{5}B. 6C5/6^{5}C. 7P5/7^{5}D. 7C5/7^{5}E. None of these
Solution follows here:

__Solution:__
Number
of possible stations to get down = 6 + 1 = 7

=>
Each person can get down at any of these 7 stations => for all five persons
there are 7*7*7*7*7 = 7

^{5}possibilities ---(1)
It
is desired that, all
five persons will get down at different stations => this is similar to
arranging 5 persons in a row of 7 places => number of possibilities is 7P5 ----(2)

Probability

= number of desired possibilities / number of all possibilities

= number of desired possibilities / number of all possibilities

= 7P5 / 7

^{5}**Answer (C)**
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