Dice order

Combinatorial Analysis
Three dices are thrown one by one. What is the probability that we witness three strictly increasing values of the dices?

Hint

This problem is possible by taking a combinatorial or conditional approach.

Answer

This problem can be approached in multiple ways.

Combinatorial analysis

(1)  

To clarify this further, checks the unique different combinations of three different numbers, where the order of the dice don't matter. However, you can order each unique set in a single increasing order, so withΒ  you automatically also check all unique strictly increasing combinations. To double check, you can write out all the increasing combinations:
123, 124, 125, 126, 134, 135, 136, 145, 146, 156, 234, 235, 236, 245, 246, 256, 345, 346, 356, 456

As you can see, there are 20 (= ) combinations.

Conditional probability

(2)  

(3)