Question

How many different three-letter initials with none of the letters repeated can people have?

Answer 1

To determine the number of different three-letter initials without repeating letters, we calculate the permutations, multiplying 26 options for the first letter by 25 for the second and 24 for the third, which gives us 15,600 unique combinations.

Step-by-step explanation:

To find out how many different three-letter initials can be made with none of the letters repeating, we use the concept of permutations. Since there are 26 letters in the English alphabet, for the first initial, we have 26 options. For the second initial, we have 25 options left (since one letter has already been used) and for the third initial, there are 24 options remaining. To find the total number of combinations, we multiply these options together.

The calculation is therefore 26 x 25 x 24, which equals 15,600 different possible three-letter initials without any repetition of the letters.

Answer 2

this is a probablity question

there are 3 slots, 26 letters of the alphabet

so in the first slot, we have 26 possible letters
2nd slot, we have 25 possible letters (we used one for the first slot)
3rd slot, we have 24 possible letters, (we used 2 for first and 2nd slot)

so in total, we have 26*25*24 or 15600 different 3 letter initials with no repeated letters