# Forgetful parents

**Discrete Mathematics**Level 3

One day, Mr and Mrs Tan decided to give an identical gift to each of their 5 children - Benedict, Bob, Brenda, Brian and Billy. To further please their children, they wrapped each gift in wrappers of their favourite colours - \({\color{green}{green}}\), \({\color{blue}{blue}}\), \({\color{red}{red}}\), \({\color{orange}{orange}}\) and \({\color{magenta}{magenta}}\) respectively.

Unfortunately, the next day, they forgot the favourite colours of their children and so distributed the gifts randomly. Let the probability that none of the 5 children receive a gift in a wrapper of their favourite colour be \(\frac{a}{b} \). If a and b have no common factors other than 1, what is a+b?

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