If the digits are not allowed to repeat in any number formed by using the digits 0 ,   2 ,   4 ,…

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 __________.

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

=4×4×3×2=96.

Asked in: JEE Main 2021 (22 Jul Shift 1)

Practice more Permutation Combination questions on Aicharya