SOLUTION: How many strings of 10 characters, such as ABCPE1234F can be made such that the first 5 characters are alphabet letters, the next 4 are digits and the last character is a

Algebra ->  Permutations -> SOLUTION: How many strings of 10 characters, such as ABCPE1234F can be made such that the first 5 characters are alphabet letters, the next 4 are digits and the last character is a       Log On


   

Question 1011597: How many strings of 10 characters, such as
ABCPE1234F
can be made such that the first 5 characters are alphabet letters,
the next 4 are digits and the last character is a letter.
Found 2 solutions by mathmate, Edwin McCravy:
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
What are the combination in PAN SERIES
ABCPE1234F
Out of 10 digits, first five digits should be alphabets(26 letters in each digit), next four digits should be Numerical Value(0-9 in each digit) and the last digit should be Alphabet(26 letters)

Solution:
There is a total of 10 digits in each "word".
If the digits and letters are allowed to repeat, then there are
n=26%5E6%2A10%2A4=3089157760000
distinct "words".
If the digits and letters are both not allowed to repeat, then there are
N=P%2826%2C5%29%2AP%2810%2C5%29=26%21%2F21%21%2A10%21%2F5%21=238702464000
words with distinct letters or digits.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

How many strings of 10 characters each, such as
ABCPE1234F
can be made such that the first 5 characters are alphabet letters,
the next 4 are digits and the last character is a letter.
(a) The characters may be repeated:

Choose the 1st character 26 ways.
Choose the 2nd character 26 ways.
Choose the 3rd character 26 ways.
Choose the 4th character 26 ways.
Choose the 5th character 26 ways.
Choose the 6th character 10 ways.
Choose the 7th character 10 ways.
Choose the 8th character 10 ways.
Choose the 9th character 10 ways.
Choose the 10th character 26 ways.

That is 26×26×26×26×26×10×10×10×10×26 = 266104 = 3089157760000 ways:

(a) The characters may not be repeated:

Choose the 1st character 26 ways.
Choose the 2nd character 25 ways.
Choose the 3rd character 24 ways.
Choose the 4th character 23 ways.
Choose the 5th character 22 ways.
Choose the 6th character 10 ways.
Choose the 7th character 9 ways.
Choose the 8th character 8 ways.
Choose the 9th character 7 ways.
Choose the 10th character 21 ways.

That is 26×25×24×23×22×10×9×8×7×21 = (26P6)×(10P4) = 
(165765600)×(5040) = 835458624000 ways.

Edwin