Question

There are 28 identical oranges that are to be distributed among 8 distinct girls. How many ways are there to distribute the oranges?

(a) ^22P7

(b) ^34C6

(c) ^35C7

(d) ^28C8

This question was posed to me during an internship interview.

The above asked question is from Counting in section Counting of Discrete Mathematics

Answer 1

Correct choice is (c) ^35C7

To elaborate: By the definition of star and bar problem, there are ^n+r-1Cr-1 possible distributions of n identical objects among r distinct bins. Now, there are n = 28 identical objects and r = 8 distinct bins. Using the formula above, there are ^35C7 ways to distribute the oranges.