Coin flipping sequence probability with biased coins

Thank you in advance to anyone willing to help me answer the following question!

I have 5 coins. Each coin is biased differently as follows:

Coin A: probability of heads = .51; probability of tails = .49
Coin B: probability of heads = .52; probability of tails = .48
Coin C: probability of heads = .53; probability of tails = .47
Coin D: probability of heads = .54; probability of tails = .46
Coin E: probability of heads = .55; probability of tails = .45

Assume that these biases are inherent to the coins themselves and not influenced by any environmental variance.

If I flip each of these coins one at a time, what is the probability that at least 3 of them will turn up heads?

I am able to wrap my feeble mind around calculating sequence probabilities when the probability of the events making up the sequence are equal. So, for example, if I wanted to know what the odds were of flipping 5 unbiased coins and getting at least 3 heads, I would simply calculate the number of possible sequences involving 3 heads or more and then divide by the number of total possible sequences.

But what do I do when the probabilities of different sequence events are biased as described above?

Again, many thanks in advance!

This is simply more calculation. For example, you must calculate the probability that A, B, C are heads and D, E are tails by multiplying the probabilities together.

Thanks for the quick response.

If I understand you correctly, what I would need to do is identify every possible sequence and then calculate the unique probability for each sequence. So, for example, the probability of coins A, B, and C coming up heads while coins D and E come up tails would be:

.51 X .52 X .52 X .46 X .45 = .029

Is that correct?

What would I do once I have done that for every possible sequence? Would I then add together the sequence probabilities for all the sequences where at least 3 coins come up heads?

You are correct. Add the probabilities for each sequence with three or more heads.