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IKMC 2017 - Grades 11-12 - Self-study Question 15

IKMC · IKMC 2017 - Grades 11-12 - Self-study

Question 15

The four faces of a regular tetrahedron are labelled with the four digits 2, 0, 1 and 7 (one digit on each face). For a game, four such tetrahedrons are used as fair dice. All four dice are thrown simultaneously. Three of the four faces of each die can then be seen from above. What is the probability that we can form the number 2017 using exactly one of the three visible digits of each die?
  1. $\frac1{256}$
  2. $\frac{63}{64}$
  3. $\frac{81}{256}$
  4. $\frac3{32}$
  5. $\frac{29}{32}$