SOLUTION: Six students, including Lauryn and D'Angelo, sit randomly in a row of six chairs. What is the probability that Lauryn is sitting in the first chair given that D'Angelo is not s

The probability under the question is the ratio of two numbers.


The denominator is the number of permutations, when D'Angelo is not sitting in the second chair.


The numerator is the number of permutations when Lauryn is sitting in the first chair AND D'Angelo is not sitting in the second chair.


As soon as you formulated this setup, the rest is just technique to calculate the answer.



Calculating the denominator.


    The number of permutations, when D'Angelo is not sitting in the second chair is equal to the total number 

    of all permutations of 6 objects (which is 6! = 6*5*4*3*2*1 = 720)  MINUS the number of all permutations, where 

    D'Angelo IS sitting in the second chair;  the last number to subtract from 720 is the number of all permutations 

    of 5 remaining persons  5! = 5*4*3*2*1 = 120.  So, the denominator is equal to 720 - 120 = 600.



Calculating the numerator.


    The numerator is equal to the total number of all permutations of 5 objects 5! = 120  (Lauryn is just fixed in the first chair !)

    MUNUS  the number of permutations of remaining 4 persons when Lauryn is sitting in the first chair and D'Angelo is sitting in the second chair.

    This number to subtract from 120 is the number of all permutations of 4 objects, i.e. 4! = 4*3*2*1 = 24.


    Thus the numerator is 120-24 = 96, and the final probability is   =  =  = 0.16 = 16%.


ANSWER.  16%.