1. ## Permutation and combination : Password generation

Hi,
I would like to know, how to solve these kind of questions.

A password must contain 2 numerals from the list {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and 4 letters from the list {a, A, b, B, c, C, d, D, e, E}. The first symbol must be a letter. Symbols may be repetitive. How many passwords can be generated meeting those conditions?

Best Regards,
RT

2. ## Re: Permutation and combination : Password generation

Originally Posted by renu
A password must contain 2 numerals from the list {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and 4 letters from the list {a, A, b, B, c, C, d, D, e, E}. The first symbol must be a letter. Symbols may be repetitive. How many passwords can be generated meeting those conditions?
There are ten ways to select the first symbol.
Each of the next five symbols can be chosen in ten ways each.
But two of those are numerals and three are alpha-symbols.
So the are $\displaystyle \binom{5}{3}$ ways to arrange those five.

What do you get for an answer?

10 000 000 !
thx.

4. ## Re: Permutation and combination : Password generation

Originally Posted by renu
10 000 000 !thx.
You got it. That is $\displaystyle 10^6\cdot\binom{5}{3}~?$

yes.