Final answer:
The number of six-letter permutations from the word NIMBLE with the second letter being a consonant and the last letter E is 96. This is calculated by considering the four possible consonants for the second position and the 24 possible arrangements of the remaining four letters.
Step-by-step explanation:
A permutation refers to an arrangement of objects in a specific order. When creating a six-letter permutation from the word NIMBLE with the constraints that the second letter is a consonant and the last letter is E, we must calculate the number of possible permutations adhering to these conditions. Initially, we have to consider that the last letter will always be 'E', which leaves us with 5 slots to fill (we are using 5 because the last letter is already determined).
Now look at the constraints for the second position: it must be a consonant. Since the word NIMBLE has 4 consonants (N, M, B, L), any of these 4 can occupy the second position. Once a consonant is placed in the second position, we then have 4 more positions to fill. The word NIMBLE without 'E' and the chosen consonant for the second position has 4 different letters left. Hence, for those 4 positions, there are 4!, or 24 permutations possible.
Ultimately, we need to multiply the number of choices for the second position (which is 4 consonants) by the number of ways to arrange the remaining 4 letters. Therefore, the total number of permutations is 4 × 4!, which equals 96 different permutations.