Even 4 dice can create havoc

Discrete Mathematics Level 5

Four regular non-identical dice are rolled. The probability that the outcome is more than \(14\) is of the form \(\dfrac{A}{B}\), where \(A\) and \(B\)

are co-prime integers.

Find the value of \(B-A\).

\(\textbf{Details and Assumptions}\)

  • Outcome means

    \( \displaystyle\sum_{n=1}^{4}(\text{number appearing on} \ n^{\text{th}} \ \text{die})\)

  • The four dice are regular ones, numbered \(1, \ 2, \ \cdots , \ 6\).

  • The four dice are not identical. You can consider them to be of four different colors.


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