Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2.
Question:

Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2.

Solution:

Number of ways in which the first digit can be filled = Number of digits available for filling it = 2  {1,2}     (Since the first one cannot be 0)

Number of ways of filling the remaining four palaces = 3 each  (as each place can be filled with either 1, 2 or 0)

By fundamental principle of counting, number of five digit numbers that can be formed $=2 \times 3 \times 3 \times 3 \times 3=2 \times 3^{4}$