Final answer:
The word 'baby' can be arranged in 12 distinguishable ways by dividing 4! by the factorial of the number of repetitions of the letter 'b', which is 2!.
Step-by-step explanation:
Calculating Distinguishable Arrangements
The number of distinguishable ways to arrange the letters of the word 'baby' involves a concept in mathematics called permutations.
Since the letter 'b' is repeated, we can't simply use 4! (four-factorial) to calculate the total number of arrangements.
Instead, we need to divide the total arrangements by the factorial of the number of times the repeated letter occurs, which is twice in this case.
The total number of arrangements without considering repetitions would be 4! or 4×3×2×1, which equals 24.
However, because the letter 'b' repeats, the correct number is calculated as follows:
- Calculate 4! to get the total arrangements if all letters were unique, which equals 24.
- Since 'b' occurs twice, we divide by 2! (the factorial of 2) to correct for the repetition.
- The final calculation is 4!/2! which simplifies to 12 unique arrangements.
Therefore, the word 'baby' can be arranged in 12 distinguishable ways.