Final answer:
To determine the number of different 'words' of various lengths that can be made from the word SQUARE, you compute the sum of permutations for each possible word length (from 1 to 6 letters). Summing the permutations (6 + 30 + 120 + 360 + 720) equals 720 unique 'words'. The correct answer is B.
Step-by-step explanation:
The question asks how many unique 'words' of any length can be formed from the letters of the word SQUARE, without repeating any letters. The word SQUARE contains 6 distinct letters, so, to answer this, we will consider the number of permutations of the letters for word lengths from 1 to 6.
For a word of length one, there are 6 choices (each letter can form a word). For a word of length two, there are 6 choices for the first letter and 5 remaining choices for the second, resulting in 6 x 5 = 30 combinations. This pattern continues up to the length of six. The total number of 'words' can be found by summing the permutations for each word length:
- 1-letter 'words': 6
- 2-letter 'words': 6 x 5
- 3-letter 'words': 6 x 5 x 4
- 4-letter 'words': 6 x 5 x 4 x 3
- 5-letter 'words': 6 x 5 x 4 x 3 x 2
- 6-letter 'words': 6 x 5 x 4 x 3 x 2 x 1
Calculating the sum of all these permutations yields 6 + (6 x 5) + (6 x 5 x 4) + (6 x 5 x 4 x 3) + (6 x 5 x 4 x 3 x 2) + (6 x 5 x 4 x 3 x 2 x 1) which equals 720. Therefore, the answer is b) 720.