How many 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of

5, and 5 is the largest digit?

Mathematics

1 answer:

Vesnalui [34]3 years ago

5 0

$5\cdot4\cdot3\cdot1+4\cdot4\cdot3\cdot1=60+48=108$

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A computer system uses passwords that contain exactly 7 characters, and each character is 1 of the 26 lowercase letters (a–z) or

Fynjy0 [20]

Answer:

0,008 or 0,8%

Step-by-step explanation:

To calculate the probability the selected password is made out only of lower-case letters, if it's only letters, we have first to find out how many passwords could be formed with only letters and with only lower-case letters.

For lowercase letters, we can make this many passwords, since for each of the 7 characters, we can pick among 26 lowercase letters:

NLL = 26 * 26 * 26 * 26 * 26 * 26 * 26

In the same fashion, for the number of passwords consisting only of letters, we can pick among 52 letters for each each character (26 lower-case, 26 upper-case):

NOL = 52 * 52 * 52 * 52 * 52 * 52 * 52

We can rewrite NOL differently to ease our calculations:

NOL = (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26) * (2 * 26)

NOL = 26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2

Now we have to find out the probability a password containing only letters (NOL) is a password containing only lowercase letters (NLL). So, we divide NLL by NOL:

$\frac{NLL}{NOL} = \frac{26 * 26 * 26 * 26 * 26 * 26 * 26}{26 * 26 * 26 * 26 * 26 * 26 * 26 * 2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2 * 2 * 2 * 2 * 2 * 2 * 2} = \frac{1}{2^{7} }$