Question

a website randomly creates an initial password for people when they first sign up for an account. the password consists of five letters, and cannot include numbers or special characters. the letters of the password cannot repeat. what is the approximate probability that a password will have no vowels? 0.00002 0.00182 0.30935 0.69065 approximate probability that the first letter of ord will be m?

Explanation:

Step1: Determine total possible passwords

There are 26 letters. For a 5 - letter non - repeating password, the number of permutations of 26 letters taken 5 at a time is given by the permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 26\) and \(r=5\). So \(P(26,5)=\frac{26!}{(26 - 5)!}=\frac{26!}{21!}=26\times25\times24\times23\times22\).

Step2: Determine favorable passwords (no vowels)

Vowels in the English alphabet are \(a,e,i,o,u\) (5 vowels). So the number of non - vowel letters is \(26- 5=21\). The number of permutations of 21 non - vowel letters taken 5 at a time is \(P(21,5)=\frac{21!}{(21 - 5)!}=\frac{21!}{16!}=21\times20\times19\times18\times17\).

Step3: Calculate probability

The probability \(P\) that a password has no vowels is the ratio of the number of favorable outcomes to the number of total outcomes.

$$
LATEXBLOCK0
$$

Wait, there is a mistake above. Let's recalculate:

$$
LATEXBLOCK1
$$

Answer:

0.30935