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Combinatorics
In how many ways can COMPUTER be spelled by moving either down or diagonally to the right showed in the figure below?? ![Very Happy :D](./images/smilies/icon_e_biggrin.gif)
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Re: Combinatorics
The answer should be 14.
Re: Combinatorics
HOW??????????????????????
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Re: Combinatorics
HOW??????????????????????
![Neutral :|](./images/smilies/icon_neutral.gif)
![Question :?:](./images/smilies/icon_question.gif)
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- Posts:1007
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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 right-down 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?![Smile :)](./images/smilies/icon_e_smile.gif)
A
B C
D E F
G H I J
From A, you have 2 choices: AB and AC (one down and the other right-down 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?
![Smile :)](./images/smilies/icon_e_smile.gif)