Question

How many different 4-letter words can be made
a) if the first letter must be B, Y, P, or M and no letter may be repeated?

b) if repeats are allowed (but the first letter is B, Y, P, or M)?

c) How many of the 4-letter words (starting with B, Y, P, or M) with no repeats end in H?

Answer 1

I'm assuming we're talking about any 4-letter combination here (doesn't have to be a real word).

For part a):
- There 4 options for the first letter (B, Y, P, M)
- There are 25 options for the second letter (any letter of the alphabet except what was used for the first letter because we can't repeat)
- There are 24 options for the third letter (any letter of the alphabet except what was used for the first and second letters because we can't repeat)
- There are 23 options for the fourth letter (any letter of the alphabet except what was used for the first, second, and third letters because we can't repeat)

These means the number of different words we can create is 4 x 25 x 24 x 23 = 55200.

Now you try part b). Just break it down by letter to come up with the number of options, then multiply everything together!