Question 1091481
#Soln
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Given d digits:
0,1,2,3,4,5,6
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To form even 3-digits without repitition & place of 50:
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1. Nos must end with either 0,2,4,6
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2. Nos must not Bgin with 0
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3. By given rule, 5 must not appear in the middle
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To ensure coverage for all of the above without contradiction, we must observe D many cases possible bit by bit
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#Case_1: 0 as unit
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When 0 is unit, any no. can occupy 1st spot:
1_0
2_0
3_0
4_0
5_0
6_0
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However:
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~ When 1,2,3,4 nd 6 re 1st digit, 5 is neva used. We'll've:
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[5][4][1] = 20
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Since 0 takes last spot, 1 of 5 nos takes 1st spot and 1 of d remainin 4 nos take 2nd spot
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~ When 5 occupies 1st spot, we'll've:
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[1][5][1] = 5
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#Case_2: Either of 2,4,6 as unit
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Digit could start with 1,3,5 & any other 2 even not used as unit
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However:
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~ When 5 isn't 1st digit, it isn't used at all:
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[4][4][3] = 48
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i.e
[1,3 or any 2 even not used up][remaining 4 nos excluding '5'][2,4 or 6]
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~ When 5 is used:
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[1][5][3] = 15
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i.e
[only 5][any other 5 excluding used up evens][2,4,6]
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Total = 20+5+48+15 = 88
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Your friend,
Francis.