If the digits are not allowed to repeat in any number formed by using the digits 0 , 2 , 4 , 6 , 8 , then the number of all numbers greater than 10 , 000 is equal to __________.

Step-by-step solution

We have to form a number greater than 10 , 000 by using the digits 0 ,   2 ,   4 ,   6 ,   8 , hence, the first place of the number can't be zero. Thus, for the first place we have 4 choices i.e. 2 ,   4 ,   6 ,   8 and the remaining places can be filled with any of the digits, thus we have respectively 4 ,   3 ,   2 ,   1 choices. Hence, using the fundamental principle of multiplication, the total numbers which are greater than 10 , 000 are = 4 × 4 ×