Question

Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be formed from the letters of the word SQUARE?

(No repeating of letters)
a) 120
b) 720
c) 5040
d) 10,080

Answer 1

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.