Dear debajeet

 

We (experts) are asked to not answer queries related to multiple questions in a single post. So next time pls take care to send just one at a time.

Here i consider only first query to be answered.

 

Total sum of 15 in 5 throws is only possible if all the 5 time we obtain 3.

 

So probalility of occurence of 3 = 1/6

 

So probability of occurence of 3 in all the 5 trials = (1/6)⁵

 

This gives probability of sum to be 15 in 5 throws = (1/6)⁵