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# How many distinct eight-character codes-with all characters distinct

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Manager
Joined: 18 Jul 2019
Posts: 54
How many distinct eight-character codes-with all characters distinct  [#permalink]

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25 Nov 2019, 06:50
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

63% (02:10) correct 38% (02:32) wrong based on 8 sessions

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How many distinct eight-character codes-with all characters distinct, containing only two numerals can be formed from A, B, C, D, E, F, 1, 2, 3, 4, such that all of them start with B and no two letters of B, D, F are together?

a) 2400
b) 36000
c) 14400
d) 43200
e) 44300
VP
Joined: 19 Oct 2018
Posts: 1174
Location: India
Re: How many distinct eight-character codes-with all characters distinct  [#permalink]

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25 Nov 2019, 10:10
Number of ways to select 8 characters of the code= 6C6*4C2=6

Total arrangements= 1*5*[6!-5!*2]= 20*5!

Total number of distinct eight-character codes= 6*20*5!=$$120^2$$=14400

CaptainLevi wrote:
How many distinct eight-character codes-with all characters distinct, containing only two numerals can be formed from A, B, C, D, E, F, 1, 2, 3, 4, such that all of them start with B and no two letters of B, D, F are together?

a) 2400
b) 36000
c) 14400
d) 43200
e) 44300
Re: How many distinct eight-character codes-with all characters distinct   [#permalink] 25 Nov 2019, 10:10
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