Mathematics - Permutation & Combination Question with Solution | TestHub

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

$=4\times 4\times 3\times 2=96.$