5-letter “words” are formed using the letters A, B, C, D, E, F, G. Find the number of possible words are possible for each of the following conditions. Not letter can be repeated in a word.

Answer 1

1. Words that start with A and end with G:

There are 5 possible choices for the second, third, fourth, and fifth letters (B, C, D, E, F), as none of them can be repeated. Therefore, there are 5^4 = 625 words that start with A and end with G.

2. Words that start with B and end with F:

Similarly, there are 5 possible choices for the second, third, and fourth letters (A, C, D, E, G), resulting in 5^3 = 125 words that start with B and end with F.

3. Words that start with C and end with E:

Following the same logic, there are 5 possible choices for the second and third letters (A, B, D, F, G), leading to 5^2 = 25 words that start with C and end with E.

4. Words that start with D and end with D:

In this case, there is only 1 possible choice for the second letter (A, B, C, E, F, G). Hence, there is only 1 word that can start with D and end with D.