A team leader has 16 tickets with upcoming deadlines. He has nine developers at his disposal. In how many ways can the team leader assign tickets to developers if each developer must get at least one ticket to avoid being out of work? There is no need to discriminate between tickets, only the number of tickets is important.

CodePudding user response：

• First distribute 9 tickets evenly as follows. You still have 7 tickets left.

  |o|o|o|o|o|o|o|o|o|

• Reset the cells.

  | | | | | | | | | |

• Distribute the remaining 7 tickets. One of all possible configurations is depicted as follows for illustration.

  |oo|ooo| | | |oo| | | |

So the total number of ways in question is the number of permutation of 7 zeros and 8 pipes. Note that the outer most pipes must be kept fixed.