We can solve this problem using fundamental principle of counting. Fundamental Principle of Multiplication : If there are two jobs such that one of them can be completed in m ways, and when it has been completed in any one of these m ways, second job can be completed in n ways; then two jobs in succession can be completed in m × n ways. By using this definition we can find the answer. The first place of the 5-digit number can be filled in 9 ways. If the second place can also be filled in 9 ways. If the third place can also be filled in 9 ways and so on. Therefore the required number of such numbers = 95. Hence, the number of 5 digit numbers in which no two consecutive digits are identical is 95.