Question

total number of 5 digit number having all different digits and divisible by 4 that can be formed using the digits {1 , 3 , 2 , 6 , 8 , 9, is equal to :

Answer 1

Answer:

The final answer is 192.

Step-by-step explanation:

Given,

{ 1 , 3 , 2 , 6 , 8 , 9 }, We need to find 5 digit numbers with the given numbers which are divisble 4.

A number is divisible by 4 if the last 2 digits are divisible by 4.

The combinations of digits which are divisible by 4 by using the above numbers = 12 , 16 , 28 , 32 , 36 , 68 , 92 , 96. The rest of the digits can be filled in 4C3 * 3! ways.

Hence the total number of 5 digits numbers which are divisible by 4

= 8 * 4! * 3!/ 1! 3! = 8 * 4 * 3 * 2 = 192

Total number of 5 digit numbers divisible by 4 = 192

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