statistics – probability about the bulb with replacement

I encounter this question

In a lot of 50 light bulbs, there are 2 bad bulbs. If we selected five bulbs and replace it after recording the results.
(a) Find the probability of at least 1 defective bulb among the 5. (With

(b) How many bulbs at least should he examine so that the probability of
finding at least 1 bad bulb exceeds 80%?

My attempt:
part (a), i find the probability by 1 – ((48C1)^(5) / (50C1)^(5)), is it correct? I’m not sure and think that there may be mistakes in it.

part (b), base on part (a) and let n be the no. of bulbs he should examine at least,
I try to calculate like this: 1 – ((48Cn)^(5) / (50Cn)^(5)) > 80%
((48Cn)^(5) / (50Cn)^(5)) < 0.2
LHS= ((48! / n!(48-n)!)^5) / ((50! / n!(50-n)!)^5)
then I am not sure is it right or not and if it is right how can i continue to find the value of n as i stuck with it.