Question

How many positive integers between \(1000\) and \(9999\) inclusive are divisible by \(5\)and by \(7\) ?

Short answer

\(257\) integers are divisible by \(5\) and \(7\).

Step-by-step solution

Given data

There are positive integers between \(1000\) and \(9999\) inclusive.

Concept used of combinatorics

Combinatorics is a branch of Mathematics which is about counting. It has many applications in other branch of Mathematics such as coding, probability. It can help us count the number of orders in which something can happen.

Find the number of solutions

The integers divisible by \(5\) and \(7\) are to be divisible by \(5 \times 7 = 35\).

\(\frac{{9000}}{{35}} = 257\)

\(257\) integers are divisible by\(5\) and \(7\).