All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Die Order (Posted on 2013-01-04) Difficulty: 3 of 5
A single die is rolled four times.

What is the probability that the numbers that come up will be in ascending order (not necessarily strictly ascending, but never a lower number after a higher)?

Intended to be solved without a computer.

  Submitted by Charlie    
No Rating
Solution: (Hide)
C(9,4) / 64 = 126 / 1296 = 7 / 72

as each choice of four integers from the range 1 through 9 corresponds with exactly one set of rolls that satisfy the desired condition.

Consider the rolls outcomes labeled as a,b,c,d. The enhanced number sets as A,B,C,D, where A=a, B=b+1, C=c+2, D=d+3.

The set A=3,B=5,C=6,D=8 corresponds to rolls of 3,4,4 and 5, and since there is inequality guaranteed by the choice of four out of nine, there is only one set, that can be placed in order, and will be in one-to-one correspondence with the original set.

Alternative Method:

As alluded to in Ady Tzidon's comment, separate track can be kept of sequences ending in 1, 2, ..., 6 and added up, starting with a sequence of 1, then 2, then 3 leading up to 4:

1+1+1+1+1+1 = 6
1+2+3+4+5+6 = 21
1+3+6+10+15+21 = 56
1+4+10+20+35+56 = 126

where each n'th term is the sum of the first n terms in the row before.

Then, of course, the sum 126 is divided by 64.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
sequel to my previous commentAdy TZIDON2013-01-05 14:15:17
re(2): No Subject re1Ady TZIDON2013-01-05 13:42:20
re: No SubjectCharlie2013-01-05 08:39:24
SolutionNo SubjectAdy TZIDON2013-01-04 18:50:51
LOLHugo2013-01-04 17:24:40
AnswerDej Mar2013-01-04 16:03:51
SolutionJer2013-01-04 14:02:54
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information