How many A.P.’s with 10 terms are there whose first term is in the s – InterviewSolution

InterviewSolution

1.

How many A.P.’s with 10 terms 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}?

Answer»

Each AP consists of a unique first term and common difference.

Number of ways to select the first term of a given set is ³C₁ = 3

Number of ways to select a common difference of given set is ⁵C₁ = 5

Hence,

Total number of AP’s possible are ³C₁ × ⁵C₁

= 3 × 5

= 15

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