How many A.P.'s with 10 temrs are there whose first term is in the set [1,2,3] and whose common difference is in the set [1,2,3,4,5] ?
There are 3 ways to choose the first form and correspondig to each such way there are 5 ways of selecting the common difference. So, required number of A.P's
= 3×5 = 15.