Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

eramsby1O1O May 26, 2024

#1**0 **

To calculate the probability that Dhruv gets exactly 7 chocolates out of the 8 chocolates Miyu is giving out to her 5 friends, we need to determine the total number of ways Dhruv can receive 7 chocolates and then divide that by the total number of ways the chocolates can be distributed.

1. Calculate the total number of ways Dhruv can receive 7 chocolates: - Dhruv can receive 7 chocolates in 1 way. - The remaining 1 chocolate can be given to any of the other 4 friends, which can happen in 4 ways.

2. Calculate the total number of ways the 8 chocolates can be distributed among the 5 friends: - Each chocolate can be given to any of the 5 friends, so there are 5^8 ways to distribute the chocolates.

3. Calculate the probability: - The probability that Dhruv gets exactly 7 chocolates is the number of ways Dhruv can get 7 chocolates divided by the total number of ways to distribute the chocolates. - Therefore, the probability is 4 / 5^8.

Hi69420 May 26, 2024