Answer to Question #278082 in Discrete Mathematics for Himanshi

Question

If 2 distinguishable dice are rolled, in how many ways can they fall? If 5

distinguishable dice are rolled, how many possible outcomes are there? How

many if 100 distinguishable dice are tossed?

Answer 1

$i)$

Since there are 2 distinguishable dice, the first dice can fall in 6 ways and the second dice can fall in 6 ways.

Therefore, there are 6*6=36 ways in which 2 distinguishable dice can fall when they are rolled.

$ii)$

When 5 distinguishable dice are rolled, each dice has 6 possible outcomes so, there are 6*6*6*6*6=6⁵=7776 possible outcomes.

Therefore, when 5 distinguishable dice are rolled, the number of possible outcomes is 7776.

$iii)$

When 100 distinguishable dice are rolled, each of the dice has 6 possible outcomes. Thus the number of possible outcomes is, 6¹⁰⁰=6.533186e⁷⁷ possible outcomes.

Therefore, when 100 dice are tossed, the number of possible outcomes is 6¹⁰⁰ .