Question

A 3 letter password from the letters a b c and d the password cannot have the same letter repeated in it how many such passwords are possible

Answer 1

`24\ passwords`

Explanation:

`Total\ available\ characters=4(a,b,c,d)\\\\ We\ want\ to\ choose\ 3\ of\ them.\\Here\ order\ matters\ (for\ example\ abc\ and\ acb\ are\ two\ different\ passwords) \\Hence\ we\ have\ to\ take\ permutation\ to\ count\ total\ possibilities.\\\\Total\ number\ of\ passwords=^4P_3\\\\Total\ number\ of\ passwords=(4!)/((4-3)!)\\\\Total\ number\ of\ passwords=(4!)/(1!)\\\\Total\ number\ of\ passwords=24`