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Fundamental Principle of Counting

How many A.P....

Question

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] ?

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Solution

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
= $3 \times 5$ = 15.

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