# Counting Problem

Consider an example of designing a security system for accessing the vault of a bank. There are 15 senior officers in the bank. To open the

vault, we need at least six of the senior officers to be present. It does

not matter which officers are present as long as there are at least six of them. To achieve this securitypolicy, each officer is issued an access

card which has m distinct codes stored on it. To open the vault, each

officer who is present puts his/her access card into the electronic lock of the vault. The computer system then collects all of the distinct

codes on the access cards, and the vault is unlocked if and only if the

set of codes collected from the cards matches the set of n (distinct)

preassigned codes.

Find the values of n and m such that n is minimal

### 1 Answer

- SteveLv 41 decade agoFavorite Answer
as we notice that for larger m (more distinct code for each officer), there will come out more combinations of code, i.e. n will be larger to open the vault.

for each officer have only 1 code, (i.e. m=1)

there are 15C6 combinations of code

therefore, n will be 15C6 for any 6 officer present to open the vault