+0  
 
0
70
1
avatar+65 

1. A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1 two 2's, and three 3's. How many possible sequences of rolls could there have been? (For example, 3,2,3,1,3,2 is one possible sequence.)

 

PS: There is a similar question like this on this website as well but they r not the same... :)

 Jul 14, 2020
edited by nicthemathwiz  Jul 14, 2020
edited by nicthemathwiz  Jul 14, 2020
 #1
avatar
+2

There should have been 60 permutations as follows:

 

[(1, 2, 2, 3, 3, 3), (1, 2, 3, 2, 3, 3), (1, 2, 3, 3, 2, 3), (1, 2, 3, 3, 3, 2), (1, 3, 2, 2, 3, 3), (1, 3, 2, 3, 2, 3), (1, 3, 2, 3, 3, 2), (1, 3, 3, 2, 2, 3), (1, 3, 3, 2, 3, 2), (1, 3, 3, 3, 2, 2), (2, 1, 2, 3, 3, 3), (2, 1, 3, 2, 3, 3), (2, 1, 3, 3, 2, 3), (2, 1, 3, 3, 3, 2), (2, 2, 1, 3, 3, 3), (2, 2, 3, 1, 3, 3), (2, 2, 3, 3, 1, 3), (2, 2, 3, 3, 3, 1), (2, 3, 1, 2, 3, 3), (2, 3, 1, 3, 2, 3), (2, 3, 1, 3, 3, 2), (2, 3, 2, 1, 3, 3), (2, 3, 2, 3, 1, 3), (2, 3, 2, 3, 3, 1), (2, 3, 3, 1, 2, 3), (2, 3, 3, 1, 3, 2), (2, 3, 3, 2, 1, 3), (2, 3, 3, 2, 3, 1), (2, 3, 3, 3, 1, 2), (2, 3, 3, 3, 2, 1), (3, 1, 2, 2, 3, 3), (3, 1, 2, 3, 2, 3), (3, 1, 2, 3, 3, 2), (3, 1, 3, 2, 2, 3), (3, 1, 3, 2, 3, 2), (3, 1, 3, 3, 2, 2), (3, 2, 1, 2, 3, 3), (3, 2, 1, 3, 2, 3), (3, 2, 1, 3, 3, 2), (3, 2, 2, 1, 3, 3), (3, 2, 2, 3, 1, 3), (3, 2, 2, 3, 3, 1), (3, 2, 3, 1, 2, 3), (3, 2, 3, 1, 3, 2), (3, 2, 3, 2, 1, 3), (3, 2, 3, 2, 3, 1), (3, 2, 3, 3, 1, 2), (3, 2, 3, 3, 2, 1), (3, 3, 1, 2, 2, 3), (3, 3, 1, 2, 3, 2), (3, 3, 1, 3, 2, 2), (3, 3, 2, 1, 2, 3), (3, 3, 2, 1, 3, 2), (3, 3, 2, 2, 1, 3), (3, 3, 2, 2, 3, 1), (3, 3, 2, 3, 1, 2), (3, 3, 2, 3, 2, 1), (3, 3, 3, 1, 2, 2), (3, 3, 3, 2, 1, 2), (3, 3, 3, 2, 2, 1)], >Total distinct permutations = 60

 Jul 14, 2020

34 Online Users

avatar
avatar
avatar