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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?

May 26, 2024

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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.

May 26, 2024