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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 repetition of letters)


A
82
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B
720
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C
1956
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D
9331
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Solution

The correct option is C $$1956$$
SQUARE 
Number of letters $$=6$$
Number of single letter word $$=6$$
Two letterd word $$=^{ 6 }{ P }_{ 2 }\\ $$
Three letterd word $$=^{ 6 }{ P }_{ 3 }$$
Four lettered word $$=^{ 6 }{ P }_{ 4 }$$
Five lettered word $$\\ =^{ 6 }{ P }_{ 5 }$$ 
Six lettered word $$\\ =^{ 6 }{ P }_{ 6 }$$
Total possible words 
$$=6+30+120+360+720+720\\ =1956\\ $$

Mathematics

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