Question

A computer password system requires 6 DIFFERENT letters (case sensitive) from the 26 alphabets. For example, AAAAAA and aaaaaa are two different passwords. Is this a PERMUTATION or a COMBINATION problem? How many passwords can be created?

Answer 1

Answer: 325

Step-by-step explanation:

Combination is a way to calculate the total outcomes of an event where order of the outcomes does not matter where as a Permutation is a way of arranging the elements of a set into a order or a sequence . Here order matters.

If we want to create password with 6 different letters then order matters.

Hence, we use permutations.

The number of passwords created is given by :-

$^{26}P_6=\dfrac{26!}{2!(26-2)!}\\\\=\dfrac{26\times25\times24!}{2\times24!}=325$

Hence, the number of passwords created = 325