Question

In how many ways a 4 letter code can be formed from the letters of English alphabet with at least one symmertric letters of the english alphabet?

Answer 1

The symmetrical alphabets are: A H I M O T U V W X Y.
The horizontally symmetrical alphabets are: B C D E H I K O X
The rotationally symmetrical alphabets are: H I N O S X

Therefore, there are 18 alphabets that are symmetric in one way or the other.

Number of ways of choosing 4 alphabets such that no symmetric alphabets are chosen = ⁸C₄

Number of ways of choosing 4 alphabets = ²⁶C₄

Number of ways of choosing 4 alphabets with at least one symmetric alphabet = ²⁶C₄ - ⁸C₄