Solution

MAGNET

Password consisting 4 letters : _ _ _ _
Ways of filling : 6*5*4*3 = 360.

Password consisting 5 letters : _ _ _ _ _
Ways of filling : 6*5*4*3*2 = 720.

Password consisting 6 letters : _ _ _ _ _ _
Ways of filling : 6*5*4*3*2*1 = 720.
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Total Ways = 1800
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Bump for further discussion
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atleast four means it can be 4,5,6...........,

so
no of ways arranging four letters from 6 = 6c4 *4! =360 (here 4! beacause we can arrange four different letters in 4! ways)

no of ways arranging five letters from 6 = 6c5 *5! =720

no of ways arranging six letters from 6 = 6c4 *6! =720

total ways are 1800
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what if repetition was allowed ? would the formulae be still used ?

when repetitions are allowed process will be different

no of 4 letter password = 6 6 6 6=\(6^4\) (each position can be filled with 6 letters)

no of 5 letter password = 6 6 6 6 6=\(6^5\) (each position can be filled with 6 letters)

no of 6 letter password = 6 6 6 6 6 6=\(6^6\) (each position can be filled with 6 letters)

total number of passwords are =\(6^4\)+\(6^5\) +\(6^6\)
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1800

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