1.A password must be chosen and it consists of 4 numbers from 0 to 9 and then 4

Question

1.A password must be chosen and it consists of 4 numbers from 0 to 9 and then 4 letters from A to Z. (example password could be 1234ABCD)

a.What is the probability that a randomly selected password will contain 1 letter repeated 4 times?

b.What is the probability that a randomly selected password will have no repeated letters and one number repeated 4 times?

c.What is the probability that a randomly selected password will have the numbers 1, 2, 3, 4 in sequence? (i.e. an example of this would be 1234ASDF)

d.If someone randomly arranged 4 numbers and 4 letters in a row what is the probability that they would form a password in the correct sequence (i.e. 4 numbers then 4 letters)?

Explanation / Answer

a) probability that a randomly selected password will contain 1 letter repeated 4 times =26 *(1/26)*(1/26)*(1/26)*(1/26)=1/263 =5.689*10-5

b)probability that a randomly selected password will have no repeated letters and one number repeated 4 times=

[10*(1/10)*(1/10)*(1/10)*(1/10)] *[(26*25*24*23)/264 ]=(0.001)*(0.785)= 7.851*10-4

c)probability that a randomly selected password will have the numbers 1, 2, 3, 4 in sequence=1/(10*10*10*10)=0.0001

d) the probability that they would form a password in the correct sequence=1/(10*10*10*10*26*26*26*26)=2.188*10-10

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