Problem with probability?

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0) is ______________.

Let X be the number of non-authentic names in a sample of 5 names. X has the binomial distribution with n = 5 trials and success probability p = 0.4

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.

The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n , p )

the mean of the binomial distribution is n * p = 2
the variance of the binomial distribution is n * p * (1 - p) = 1.2
the standard deviation is the square root of the variance = 鈭?( n * p * (1 - p)) = 1.095445

The Probability Mass Function, PMF,
f(X) = P(X = x) is:

P( X = 0 ) = 0.07776 鈫?answer
P( X = 1 ) = 0.2592
P( X = 2 ) = 0.3456
P( X = 3 ) = 0.2304
P( X = 4 ) = 0.0768
P( X = 5 ) = 0.01024