Combinatorics
Combinatorics
In how many ways can COMPUTER be spelled by moving either down or diagonally to the right showed in the figure below??
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 Posts: 62
 Joined: Sun Mar 30, 2014 10:40 pm
Re: Combinatorics
The answer should be 14.
Re: Combinatorics
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Re: Combinatorics
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 samiul_samin
 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: Combinatorics
Count carefully acclrding the question.
Re: Combinatorics
If repeated letters distract you, replace these in the following way, because the question basically asks you to choose and count properly:
A
B C
D E F
G H I J
From A, you have 2 choices: AB and AC (one down and the other rightdown diagonally).
From each of AB and AC, you have also 2 choices: ABD, ABE and ACE, ACF. Total count up to the third row is, therefore, 4 or (2 × 2)
From each of ABD, ABE, ACE, and ACF, you have also 2 choices.
Can you see a pattern now and complete?
A
B C
D E F
G H I J
From A, you have 2 choices: AB and AC (one down and the other rightdown diagonally).
From each of AB and AC, you have also 2 choices: ABD, ABE and ACE, ACF. Total count up to the third row is, therefore, 4 or (2 × 2)
From each of ABD, ABE, ACE, and ACF, you have also 2 choices.
Can you see a pattern now and complete?