Final answer:
To find the number of arrangements of 'MATHEMATICS' containing 'ATTIC', treat 'ATTIC' as one unit, then arrange the remaining letters, accounting for the repetition of 'M'. The result is 6! divided by 2!, which equals 360 unique arrangements.
Step-by-step explanation:
To determine the number of possible arrangements of the letters in the word MATHEMATICS that contains the word 'ATTIC' spelled left to right, we must consider 'ATTIC' as a single unit. We then have the remaining letters M, A, H, E, M, T, S to arrange around 'ATTIC'. Since the letter 'M' appears twice, we need to account for this repetition.
When we treat 'ATTIC' as one unit, we have six units to arrange, 'ATTIC', M, A, H, E, T, S. There are 6! (six-factorial) ways to arrange these six units. However, we also have to consider the repeated M. To account for this repetition, we take the total arrangements and divide by 2! (two-factorial), because there are 2 M's.
The calculation is 6! / 2!, which simplifies to 6×5×4×3×1 / 2×1. This gives us 360 unique arrangements where 'ATTIC' is spelled left to right. In conclusion, there are 360 arrangements.