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

#### frederic1

##### New Member
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

Thanks a lot guys :tup:

Last edited:

#### Dason

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?

#### frederic1

##### New Member
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

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?

#### frederic1

##### New Member
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

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?

#### frederic1

##### New Member
I don't know why you're summing a whole bunch of stuff.
i'm not very good at statistics

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 ?

#### kenasto

##### New Member
And there there 20 different positions for the digit, so how about 26^19 * 10 * 20 ?

#### Dason

And there there 20 different positions for the digit, so how about 26^19 * 10 * 20 ?
Yup. You need to account for the different places it could go. Since after all
1aaaaaaaaaaaaaaaaaaa is different than a1aaaaaaaaaaaaaaaaaa

#### frederic1

##### New Member
**** i didn't think that the position could influence the possible combinations so much ! you guys are real stats experts :tup:

#### Dragan

##### Super Moderator
.....you guys are real stats experts :tup:
Well, maybe... but I am still not satisfied with the proposed attempts to solve this problem.