ISRO | ISRO CS 2018 | Question 2

A class of 30 students occupy a classroom containing 5 rows of seats, with 8 seats in each row. If the students seat themselves at random, the probability that the sixth seat in the fifth row will be empty is
(A) 1/5
(B) 1/3
(C) 1/4
(D) 2/5


Answer: (C)

Explanation: There are 5 rows with 8 seats in each row.
So, there are total 40 seats
If sixth seat in the fifth row is empty then 30 students have 39 choices of seats
So, ways to choose from given choices = ³⁹C₃₀
But, total ways to choose = ⁴⁰C₃₀

Probability = ³⁹C₃₀ / ⁴⁰C₃₀
Probability = 1/4

Option (C) is correct.

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