**Question:**

How many arithmetic progressions with 10 terms are there whose first term in the set {1, 2, 3} and whose common difference is in the set {2, 3, 4}?

**Solution:**

Given: Two sets: $\{1,2,3\} \&\{2,3,4\}$

To find: number of A.P. with 10 n terms whose first term is in the set $\{1,2,3\}$ and whose common difference is in the set $\{2,3,4\}$

Number of arithmetic progressions with 10 terms whose first term are in the set $\{1,2,3\}$ and whose common difference is in the set $\{2,3,4\}$ are: $3 \times 3=9$

( 3 because there are three elements in the set $\{1,2,3\}$ and another 3 because there are three elements in the set $\{2,3,4\}$ )