Answer:
The correct answer is [tex]\left[\begin{array}{ccc}26\\6\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}6\\3\end{array}\right][/tex].
Step-by-step explanation:
Total number of alphabets the system can use = 6
In English language there are 26 alphabets and we are to use any 6 of them. Thus this can be done in [tex]\left[\begin{array}{ccc}26\\6\end{array}\right][/tex] ways.
A password is to be made for a security system using the above 6 letters and no letter can be used more than once.
Thus number of possible ways of making passwords of three letters using the above six letters are [tex]\left[\begin{array}{ccc}6\\3\end{array}\right][/tex].
Total number of possible ways to choose 6 alphabets and make a password of 3 letters are [tex]\left[\begin{array}{ccc}26\\6\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}6\\3\end{array}\right][/tex].
