(b) To log on to a certain computer account, the user must type in a 5-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 5-letter passwords are possible? (There are 26 letters in the alphabet.)
Question
(b) To log on to a certain computer account, the user must type in a 5-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 5-letter passwords are possible? (There are 26 letters in the alphabet.)
Solution
To solve this problem, we need to use the concept of permutations.
A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by the formula: P(n, r) = n! / (n-r)!
In this case, we have 26 letters and we want to arrange 5 of them in a specific order without repetition. So, n = 26 and r = 5.
Substituting these values into the formula, we get:
P(26, 5) = 26! / (26-5)!
= 26! / 21!
= (26 * 25 * 24 * 23 * 22)
= 7,893,600
So, there are 7,893,600 possible 5-letter passwords.
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