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The code for a particular combination lock can only include

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chajaemin90
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The code for a particular combination lock can only include [#permalink] New post   16 Sep 2020, 13:48
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The code for a particular combination lock can only include letters, symbols, and digits from a selection of 7 letters, 3 digits, and 5 symbols. A valid code for the lock must consist of exactly 2 letters, 1 symbol, 1 digit, and 1 symbol, in that order, and repetition is allowed. How many different codes are possible?

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3675
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njeshi
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Re: The code for a particular combination lock can only include [#permalink] New post   16 Sep 2020, 15:51
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#total: 7 letters, 3 digits, and 5 symbols
#needed 2 letters, 1 symbol, 1 digit, and 1 symbol
=> C(7,2) x C(5,1) x C(3,1) x C(4,1)(already chose 1 symbol so 4 left) = 21x5x3x4 = 1260
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Re: The code for a particular combination lock can only include [#permalink] New post   19 Oct 2020, 02:48
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3675 ways. as repetition is allowed.
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Re: The code for a particular combination lock can only include [#permalink] New post   19 Oct 2020, 08:11
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Since repetition is allowed we have
7*7*5*3*7=3675

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endurance
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Re: The code for a particular combination lock can only include [#permalink] New post   08 Nov 2020, 07:32
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L L S D S => this order must be maintained, here repetition is also allowed

therefore, the number if code will be= 7*7*5*3*5= 3675
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BeeKay
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Re: The code for a particular combination lock can only include [#permalink] New post   08 Nov 2020, 21:05
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endurance wrote:
L L S D S => this order must be maintained, here repetition is also allowed

therefore, the number if code will be= 7*7*5*3*5= 3675



Shouldn't we also multiply 3675 with 5! because of the arrangement of 5 selected numbers itself ?

Please guide me.
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endurance
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Re: The code for a particular combination lock can only include [#permalink] New post   08 Nov 2020, 21:19
here the order is defined, thus you do not need to multiply by 5!
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Re: The code for a particular combination lock can only include [#permalink] New post   25 Feb 2021, 23:57
if the question says that order matters, how would it differ?
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Re: The code for a particular combination lock can only include [#permalink] New post   26 Feb 2021, 06:14
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gd2906 wrote:
if the question says that order matters, how would it differ?


You mean when the order doesn't matter?
In that case - You multiply it with \(\frac{5!}{{2! 2!}} = 30\)
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