Final answer:
The probability that a specific pair of books will not be placed together in a random arrangement of 25 books is 23/25.So, So, the probability that a particular pair of books shall never be together is 23/25. correct option is option is D) 2325
Step-by-step explanation:
The problem requires determining the probability that in a random arrangement of 25 books, a particular pair of books will not be placed together. We can solve this problem using complementary probability. The total number of arrangements of 25 books is 25!.
To find the number of arrangements where the pair is together, we treat the pair as one item, leading to 24! arrangements for the 'pair' and the remaining books, and 2! arrangements for the two books in the pair. Therefore, the pair can be arranged in 24! * 2! ways.
The probability of the pair being together is (24! * 2!)/25!, and the probability of the pair not being together is 1 minus this value.
To calculate the probability, we simplify (24! * 2!)/25! to 2/25 by canceling out the 24! in the numerator and denominator. Then, 1 - 2/25 gives us 23/25. So, the probability that a particular pair of books shall never be together is 23/25.
The correct option is option is D) 2325