The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2 , 3 , 4 , 5 , 6 (repetition of digits is not allowed) and divisible by 55 is _____.

Step-by-step solution

Given number should be 4 digit numbers between 1012   &   23421 and can be formed using the number 2 ,   3 ,   4 ,   5 ,   &   6 and should be divisible by 55 CASE I: When number has 4 digit, Now for divisibility by 55 , number should be divisible by 5 and 11 both Also, for divisibility by 11 for below figure, Now fixing d = 5 the total possible cases for a , b , c will be 6 , 4 , 3 , 3 , 4 , 6 , 2 , 3 , 6 , 6 , 3 , 2 , 3 , 2 , 4   &   4 , 2 , 3 CASE II: When