Final answer:
To find the number of arrangements of the word "hollow", where the two 'l' letters do not come together, subtract the arrangements with the 'l' letters together from the total unrestricted arrangements. The answer is 120 ways.
Step-by-step explanation:
The question asks for the number of ways the letters in the word "hollow" can be arranged so that the two 'l' letters do not come together. The total arrangements of the letters without any restriction is 6!/2! since the 'o's are indistinguishable. To find the arrangements where 'l' letters don't come together, we subtract the number of arrangements where 'l' letters are together from the total arrangements.
Calculating the total arrangements: 6!/2! = (6 × 5 × 4 × 3 × 2 × 1)/(2 × 1) = 360.
Next, we calculate the arrangements where 'l' letters are together by treating them as a single unit: (5! arrangements for the rest of the letters including the 'll' unit) × 2! (arrangements for 'l's within the unit) = 5! × 2 = 120 × 2 = 240.
Finally, subtract the arrangements with 'l' letters together from the total: 360 - 240 = 120. So, there are 120 ways to arrange the letters of the word "hollow" so that the 'l' letters do not come together.