Understanding the Problem
To find the 70th word formed by the letters of "TOWER" in dictionary order, we first list the letters: E, O, R, T, W.
Step 1: Counting Arrangements
- The letters in "TOWER" are unique, so we can calculate the total arrangements as 5! (factorial of 5).
- 5! = 120 total arrangements.
Step 2: Arranging in Dictionary Order
The letters in alphabetical order are: E, O, R, T, W.
Step 3: Counting Words Starting with Each Letter
- Starting with E:
- Remaining letters: O, R, T, W = 4! = 24 words.
- Starting with O:
- Remaining letters: E, R, T, W = 4! = 24 words.
- Total so far (E + O): 24 + 24 = 48 words.
- Starting with R:
- Remaining letters: E, O, T, W = 4! = 24 words.
- Total so far (E + O + R): 48 + 24 = 72 words.
Since 70 is between 49 and 72, the 70th word starts with R.
Step 4: Words Starting with R
Remaining letters are E, O, T, W. We now arrange these letters in alphabetical order: E, O, T, W.
- Starting with RE:
- Remaining letters: O, T, W = 3! = 6 words (49-54).
- Starting with RO:
- Remaining letters: E, T, W = 3! = 6 words (55-60).
- Starting with RT:
- Remaining letters: E, O, W = 3! = 6 words (61-66).
- Starting with RW:
- Remaining letters: E, O, T = 3! = 6 words (67-72).
Conclusion: Finding the 70th Word
The 70th word is the 4th word starting with RW, which is “RWOET.”
Thus, the 70th word in the dictionary arrangement of "TOWER" is RWOET.