10
Starting with three different letters, six two-letter combinations can be made, if the order of the two letters is important. Only three combinations can be made if the order of the two letters is not important. Example: ABC AB AC BA BC CA CB - six variations But if (for your purposes) BA is the same as AB, Then there are only three: AB AC BC
45
4! = 4*3*2*1 = 24 of them.
17,576 possible combinations * * * * * Not quite! This is the total number of permutations of 3 letters out of 26. AAB is counted as being different from ABA or BAA. But these are the same combinations. Thus there are 26 combinations of just one letter. 26*25 combinations of two letters and 26*25*24/(3*2*1) of three. In all, that makes 26 + 650 + 2600 = 3276
I assume you mean no repetition to be ABC and not ABA OR AAB. That being said this is very straight forward. The first position can potentially have any of the 26 letters. the second position can only have 1 of 25 possible letters because one letter has already be selected for the first position. And the final position can only have 1 of 24 possible letters because two letters have already been selected for the first two positions. Just multiply the number of possibilities for each position together and you have your answer. 26 * 25 * 24 = 15600 possible combinations.
In a permutation problem such as this, there are six spaces, each of which could be one of two letters. This means there are sixty-four possible combinations. The two obvious combinations are aanwmn and ccpyop. Looking at those, the word is then canyon.
6X6=36
262/2*102/2 = 67600/4 = 16900
Normally, there would be 5!=120 different permutations* of five letters. Since two of the letters are the same, we can each of these permutations will be duplicated once (with the matching letters switched). So there are only half as many, or 60 permutations.* (the correct terminology is "permutation". "combination" means something else.)
3
If the first two letters must be an S or a T, then there are three remaining places that can be one of 26 letters. This is equal to 26 * 26 * 26 * 2, or 35,152 possible combinations.
For the 4 letters, there are 12 discrete pairs of letters, but only 6 unique pairs. FI, FS, FH (and the mirrors IF, SF, HF) IS, IH (and the mirrors SI and HI) SH (and the mirror HS)