Suppose the 5 friends are A,B,C,D,E, where D is Dhruv. In the "successful" cases, some of them will not get any chocolates, if Dhruv has to get at least 6 and there are only 8 chocolates. There are 4 cases where Dhruv gets at least 6 chocolates: Case 1. Dhruv gets 6 chocolates and 1 of the other 4 gets both the other 2 chocolates. Choose the 1 friend to get the other 2 chocolates in 4 ways. Case 2. Dhruv gets 6 chocolates and 2 of the other 4 get 1 chocolate each. Choose the 2 friends to get 1 chocolate each in C(4,2) = 6 ways. Case 3. Dhruv gets 7 chocolates and 1 of the other 4 gets the other 1 chocolate. Choose the 1 friend to get the other 1 chocolate in 4 ways. Case 4. Dhruv gets all 8 chocolates and the other 4 get none. That's 1 way. That's 4+6+4+1=15 "successful" cases. To find all the possibilities, make a line of 8 stars and 4 bars, like this sample illustration: ***||***|**| A gets the same number of chocolates as the number of bars left of the left-most bar, which in the sample illustration is 3 B gets the same number of chocolates as the number of stars between the 1st and 2nd bars, which in the sample illustration is 0. C gets the same number of chocolates as the number of stars between the 2nd and 3rd bars, which in the sample illustration is 3. D gets the same number of chocolates as the number of stars between the 3rd and 4th bars, which in the sample illustration is 2. E gets the same number of chocolates as the number of stars to the right of the 4th bar, which in the sample illustration is 0. There are 8 stars and 4 bars. That's 12 things, where the 8 stars are indistinguishable from each other, and also the 4 bars are also indistinguishable from each other. So the number of ways the chocolates can be divided is. So the probability that Dhruv gets at least 6 chocolates is 15/495 which reduces to 1/33. Edwin