Discrete Mathematics Solved Problems

This discrete mathematics solved problems set contains simple and complex problems related to articles arrangements, possible ways of alphabets in the specific word. Some very interesting problems

Solved Question on Discrete Mathematics -

Question: How many three digit numbers are there with distinct digits with each digit even, i) with 0 and ii) without 0?
Answer: Here we are required to form three-digit numbers with distinct each digit even.
The even digits are 0, 2, 4, 6, and 8.


The digits used are 0, 2, 4, 6, and 8.
The hundred's place can be filled in 4 ways (excluding zero).
The ten's place can be filled in again in 4 ways (including zero).
The unit's place can be filled in 3 ways.
Hence, by the fundamental principle of counting, the number of three
digit numbers = 4 x 4 x 3 = 48.

ii) Without 0
The digits used are 2, 4, 6, and 8.
The hundred's place can be filled in 4 ways.
The ten's place can be filled in 3 ways and the unit's place can be filled
in 2 ways.
Hence, by the fundamental principle of counting, the number of three digit numbers = 4 x 3 x 2 = 24.