Let random variable X be the number of 7s in a line of 50 slots.
The probability of getting exactly k successes in n trials is given by
P(X = k) = C(n, k) pk(1-p)n-k
For this problem
n = 50
k = 5
p = 0.1
So the probability of finding exactly five 7s in a line with 50 slots is
P(X = 5) = C(50, 5) (0.1)5(1-0.1)45
= 0.1849