There are 4 characters.They can be arranged within themselves so they can be arranged in 24 ways.[Note : The formula for this is n! if there are n characters.]
Since there are 4 letters, they can be arranged 4! ways (4*3*2*1) or 24 ways.
If no digit can be repeated then there are 5 combinations, abcd, abce, abde, acde and bcde. If you regard abdc as different from abcd then each of the 5 basic sets could be arranged 24 ways and the total would be 120 combinations.
Six ways. Starting clockwise from A, they are: ABCD, ABDC, ACBD, ACDB, ADBC and ADCB. Any other way is simply a rotation of one of these.
10
abcd
There would be 4 different gametes: ABCD, ABcD, ABc, and ABcD. Each gamete represents a unique combination of alleles for each gene.
4
Without repeats, 24. With repeats, 256.
This depends on if you want repeats or not (or the state you are in) with repeats it is: 26x26x26x10x10= 1,757,600 without repeats it is: 26x25x24x10x9=1,560,000
how many ways can 8 letters be arranged
Allowing repeats, but not leading 0s, the answer is 9,000,000,000