# How many 4-digit numbers that can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

By Raj Vimal|Updated : October 11th, 2022

(A) 216

(B) 60

(C) 24

(D) 25

There are 60 four digit numbers that can be formed from the digits 2, 3, 5, 6, 7 and 9, divisible by 5 and none of the digits is repeated. Given digits = 2, 3, 5, 6, 7 and 9. Using the concept of the Divisibility rule of 5: If a number's unit digit is either 5 or 0, it is divided by 5.

### 4 Digit Numbers Formed From 2,3,5,6,7 and 9

Consider the calculation part, Unit digit can only be 5.

A unit slot can only be filled in 1 way.

Places left open may be filled by 2, 3, 6, 7, or 9.

There are five different ways to replace the number 10.

Due to the fact that numbers cannot be duplicated, there are four ways to fill the hundredth place.

A four-digit number can be filled in its initial position in one of three ways.

Total numbers that can be formed = 1 × 5 × 4 × 3 = 60

∴ 60 four-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9.

Summary:

How many 4-digit numbers that can be formed from the digits 2, 3, 5, 6, 7, and 9, which are divisible by 5, and none of the digits is repeated? (A) 216 (B) 60 (C) 24 (D) 25

Divisible by five digits 2, 3, 5, 6, 7, and 9, none of which are repeated, can be combined to create 60 four-digit numbers. These numbers are easily divisible by 5 without getting repeated digits.