Probability-1 (XAT-2009)

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.6P5/6⁵        B. 6C5/6⁵       C. 7P5/7⁵       D. 7C5/7⁵                   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 = 7⁵ 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

= 7P5 / 7⁵

 Answer (C)