A pair of dice is thrown 5 times then probability of getting doublet exactly twice I am given 2 identical unbiased dice which are thrown simultaneously 5 times , then what will be probability of getting doublet exactly twice ? Since we we can have any number in first dice corresponding to which there should be same number in other dice for doublet $$(\frac{6}{6}.\frac{1}{6}). (\frac{6}{6}.\frac{1}{6}). (\frac{6}{6}.\frac{5}{6}). (\frac{6}{6}.\frac{5}{6}). (\frac{6}{6}.\frac{5}{6}). $$ Is my method correct ? Will there be multiplication or addition between all 5 probabilities? I am certain that since task is performed in one process there should be multiplication

You have computed the probability that (for example) the first and second throws of the pair of dice produce pairs (doublets) and the others do not.

It could also be the case that the first throw is a pair, the second is not, but the third throw is (and the remaining two are not). This is also an event where you get a pair exactly twice, but it is disjoint from the other event.

So you must also consider how many possible different events you could be looking for. The two pairs could come anywhere within the sequence of throws.