In the English alphabet, there are 7 capital letters that look the same after being rotated 180∘. Those letters are H, I, N, O, S, X, and Z. How many different 3 letter "words" can be made from these letters such that when the word is rotated 180∘, the resulting word is the same?

To solve this problem, we need to consider all possible combinations of the given letters to form three-letter "words" that remain the same when rotated 180 degrees.

Here's the step-by-step approach:

1. Identify the seven letters that remain the same when rotated 180 degrees: H, I, N, O, S, X, and Z.

2. Select three letters from the given set. Since there are seven choices for each position, we can calculate the number of combinations using the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items selected.

In this case, n = 7 (the total number of letters that remain the same when rotated 180 degrees), and r = 3 (the number of letters in each word). Plugging the values into the formula:

7C3 = 7! / (3!(7-3)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

Therefore, there are 35 different three-letter "words" that can be made using these letters such that they remain the same when rotated 180 degrees.

It’s not right

It’s not right jishca

Clearly the 1st and 3rd letter must be the same, but the middle can be any of the 7 letters

number of ways = 7 x 7 x 1 = 49

SOS