Question

The number of words which can be formed out of the letters of the word ARTICLE,

Answer 1

Answer:

13699 if repetition of letters is not permitted

960799 if repetition of letters is permitted

Step-by-step explanation:

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Without repetition:

1 letter words: 7

2 letter words: 7 choices for first letter, then 6 for second letter, so total is 7 x 6 = 42

3 letter words: 7 x 6 x 5 = 210

4 letter words: 7 x 6 x 5 x 4 = 840

5 letters: 2520

6 letters: 5040

7 letters: 5040

Total number of words: 7 + 42 + 210 + 840 + 2520 + 5040 + 5040 = 13699

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With repetition:

1 letter words: 7

2 letter words: 7 choices for first letter, then 7 for second letter, so total is 7x7 = 49

3 letters: 7 x 7 x 7 = 343

4 letters: 2401

5 letters: 16807

6 letters: 117649

7 letters 823543

Total number of words: 960799