Baz, may I ask if you understand any of these problems?
You seem to be gussing at answers.
This time I shall give you the answer as it might appear in the 'back of the book'
Can you explain that to us?
Can any check out this one?
A password for the computer is a string of digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
and/or letters
a,b,c,. . . ,x,y,z
(there are 26 different letters). The password must obey the following
rules:
(a) the length of the password must be exactly 8 characters;
(b) the password must contain at least one digit, and no more than
three digits.
What is the number of different passwords you can form?
I think number of different passwrds are
10x26! + 10x10x25! +10x10x10x24!
3 things to note, baz.....
1. Do you realise you are making a password violating rule (a) ?
2. In forming your 27-character password, do you realise that you are only arranging the letters ?
3. Do you also realise that you are allowing the digits to be used multiple times but not the letters ?
Plato you have given the answer for the case where repitition is allowed.
Case1 (1 digit allowed)
10 ways of choosing one (10 digits )of the 8 spots , 26^7 ways of choosing remaining spots , (8 binom 1) ways of choosing 8 taking 1 at a time.
by product rule all the above outcomes are multiplied.
Similarly we will workout ways for remaining two cases and them .