Well if Louis = L2, Lucas = L1, Garcelle = G and Sheryl = S, these are the possibilities. S,L1,G,L2 S,G,L1,L2 S,G,L2,L1 G,S,L1,L2 G,S,L1,L2 G,L1,S,L2 G,L2,S,L1 G,L1,L2,S G,L2,L1,S This is 9 possibilities so 9. I might be wrong though.
Applying the Central Limit Theorem you approximate the distribution of the sample proportion to normal to obtain the statistic to use.
You are asked to estimate the population proportion of televisions that didn't require repairs with a confidence interval, the formula is:
^ρ±* √[(^ρ(1-^ρ))/n]
= = 2.58
0.78±2.58* √[(0.78(1-0.78))/390]
0.0541
[0.726;0.834]
With a confidence level of 99% you'd expect that the interval [0.726;0.834] contains the true value of the proportion of ColorSmart-5000 that didn't need repairs after 5 years of use.