Imagine I have a matrix in Excel, i.e., an array in the interval A1:E5. Each cell has either a 0 or a 1. How can I find the position of a random zero in that array?

I saw that using the Excel function SUMPRODUCT, I would be able to find the row and column to which a certain value corresponded. The problem is that this procedure would only work if the value I was looking for was unique.

Here's an example of what I want:

Consider that my data is

row | A | B | C | D | E |
---|---|---|---|---|---|

1 | 0 | 1 | 0 | 1 | 1 |

2 | 0 | 0 | 0 | 1 | 1 |

3 | 1 | 1 | 1 | 1 | 1 |

4 | 1 | 1 | 1 | 1 | 0 |

5 | 0 | 1 | 1 | 1 | 1 |

I would like to have a function that would select a random output from the set `{(1,A),(1,C),(2,A),(2,B),(2,C),(4,E),(5,A)}`

.

By function I mean an expression in an Excel cell.

Anyone knows how to do this?