19 lowercase letters + 1 single digit number = possible combinations ?

#1
Hi everybody and happy new year too all :tup:

I've just discovered this forum today and I have one thing to say : AWESOME ! :)

I have trouble solving this :

How many combinations are possible for a 20-Caracters String that contains :
- 19 lowercase letters (a to z)
- 1 single-digit number (0 to 9) placed randomly in the string

examples of generated strings are :
abcdefghijklmnopqrs1
aaaaaaaaa9aaaaaaaaa
2yyyyyyyyyzzzzzzzzz
etc.

I'd like to know how many different strings are possible :confused:

Thanks a lot guys :tup:
 
Last edited:

Dason

Ambassador to the humans
#2
Have you done any work on the problem so far? If so, what have you done? It's a relatively simple counting problem.

Could you do the problem if you ignored the randomly placed number? In other words could you figure out how many 19 characters strings there are that only contain lower case letters?
 
#3
hey Dason thanks for your reply :tup: a friend of mine made some calculations and told me that there were 20 million possibilities but I don't believe him, I think that there are much more
 

Dason

Ambassador to the humans
#4
Yes there are indeed much more.

Have you done any work on the problem so far? If so, what have you done?

Could you do the problem if you ignored the randomly placed number? In other words could you figure out how many 19 characters strings there are that only contain lower case letters?
 
#5
could you do the problem if you ignored the randomly placed number? In other words could you figure out how many 19 characters strings there are that only contain lower case letters?
Am I right to say :
26 + 26^2 + 26^3 + 26^4 + 26^5 + 26^6 + 26^7 + 26^8 + 26^9 + 26^10 + 26^11 + 26^12 + 26^13 + 26^14 + 26^15 + 26^16 + 26^17 + 26^18 + 26^19

26
+ 676
+ 17576
+ 456976
+ 11881376
+ 308915776
+ 8031810176
+ 208827064576
+ 5429503678976
+ 141167095653376
+ 3670344486987776
+ 95428956661682176
+ 2481152873203736576
+ 64509974703297150976
+ 1677259342285725925376
+ 43608742899428874059776
+ 1133827315385150725554176
+ 29479510200013918864408576
+ 766467265200361890474622976

= 797,125,955,808,376,366,093,607,894
 

Dason

Ambassador to the humans
#6
I don't know why you're summing a whole bunch of stuff. The right answer is one of your terms but I don't quite understand your logic. For the problem I asked (how many 19 character strings consisting of only lower case letters are there) the answer is 26^19. For each of the 19 spots in the 19 character string there are 26 different choices for letters. This gives 26*26*...*26 = 26^19 total possibilities. Much larger than 20 million. Can you figure out how to add in the single number for the 20 character string?
 
#7
I don't know why you're summing a whole bunch of stuff.
i'm not very good at statistics :(

The right answer is 26^19.
thanks mate :) :) :)

For each of the 19 spots in the 19 character string there are 26 different choices for letters. This gives 26*26*...*26 = 26^19 total possibilities. Much larger than 20 million. Can you figure out how to add in the single number for the 20 character string?
I think I fugured it out :) a 1 digit number is 10 different choices (0..9) so maybe the forumula is : 26^19 * 10 ? Am I right ? :)