A class photograph is to be taken with ten students
MATHEMATICS · Multi-part · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations
Problem
A class photograph is to be taken with ten students, including Arjun (A) and Bhavna (B), standing in a single straight line. Solve the following sub-questions, giving complete justification for each answer:
(i) Determine the total number of possible linear arrangements of the ten students.
(ii) Find the number of arrangements if Arjun must stand at the extreme left position and Bhavna must stand at the extreme right position.
(iii) Calculate the number of arrangements in which Arjun and Bhavna occupy the two extreme positions of the line, but their exact left–right order may be interchanged.
(iv) Using your results, compute the probability that, in a random arrangement of the ten students, Arjun and Bhavna occupy the extreme positions (in either order). Express your answer as a simplified fraction.