Question

How many 4-letter passords can be made using the letters A thought Z if...

Answer 1

Answer:

a.)The total 4-letters passwords when repetition of letters is allowed are 456976

b.)The total 4-letters passwords when repetition of letters is not allowed are 358800

Step-by-step explanation:

Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.

How many 4-letter passwords can be made using the letters A throught Z if...

a)Repetition of letters is allowed?

There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are $26^{4} =456976$

b) Repetition of letters is not allowed?

If repetition of  letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation $nP_{k} =\frac{n!}{(n-k)!}$

The total 4-letters passwords when repetition of letters is not allowed are $26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800$

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