A woman has 14 identical pens to distribute among a group of 10 distinct students. How many ways are there to distribute the 14 pens such that each student gets at least one pencil?(a) ^15C10(b) ^10C5 * 11(c) ^15C8 * 4!(d) ^13C9This question was posed to me in an interview for internship.The query is from Counting topic in chapter Counting of Discrete Mathematics

A woman has 14 identical pens to distribute among a group of 10 distin

1.	A woman has 14 identical pens to distribute among a group of 10 distinct students. How many ways are there to distribute the 14 pens such that each student gets at least one pencil?(a) ^15C10(b) ^10C5 * 11(c) ^15C8 * 4!(d) ^13C9This question was posed to me in an interview for internship.The query is from Counting topic in chapter Counting of Discrete Mathematics
Answer» Right answer is (d) ^13C9 To EXPLAIN: For this type of problem, n>=r MUST be true and so according to stars and bars model, the number of possible arrangements of stars and bars is n-1Cr-1 or equivalently, there are ^n-1Cr-1distributions of n identical objects into r DISTINCT non-empty BINS. In this example, there are n = 14 identical objects to be distributed among r=10 distinct bins. Using the above FORMULA, the number of possible distributions is ^13C9.

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