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  • A permutation lock will open if the right choice of 4 numbers (from 1 to 20) is selected. How many lock permutations can be made assuming no number is repeated?<div class='qna-option'

A permutation lock will open if the right choice of 4 numbers (from 1 to 20) is selected. How many lock permutations can be made assuming no number is repeated?

Option: 1

116280

 

 


Option: 2

6840

 

 


Option: 3

7820

 


Option: 4

115280


Answers (1)

best_answer

We have 100 digits and arrange four of them. We have  ^{20}P_{4}    options.

^{20}P_{4}=\frac{20!}{\left ( 20-4 \right )!}


^{20}P_{4}=\frac{20!}{16!}

^{20}P_{4}=\frac{20\times 19\times 18\times 17\times 16!}{16!}

 ^{20}P_{4}=20\times 19\times 18\times 17  

  ^{20}P_{4}=116280

Therefore, the total number of ways lock permutations can be made is 116280 ways.

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Pankaj

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