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Omni-MATH / Let n be a positive integer. Compute the number of words w that satisfy the following three properties. 1. w consists of n letters from the alphabet {a,b,c,d}. 2. w contains an eve…

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problem

Let nn be a positive integer. Compute the number of words ww that satisfy the following three properties. 1. ww consists of nn letters from the alphabet {a,b,c,d}.\{a,b,c,d\}. 2. ww contains an even number of aa's 3. ww contains an even number of bb's. For example, for n=2n=2 there are 66 such words: aa,bb,cc,dd,cd,dc.aa, bb, cc, dd, cd, dc.
Plain-text mathematical notation (without MathML)
Let n be a positive integer. Compute the number of words w that satisfy the following three properties.

1. w consists of n letters from the alphabet {a,b,c,d}.

2. w contains an even number of a's

3. w contains an even number of b's.

For example, for n=2 there are 6 such words: aa,bb,cc,dd,cd,dc.
Original LaTeX notation
Let $n$ be a positive integer. Compute the number of words $w$ that satisfy the following three properties.

1. $w$ consists of $n$ letters from the alphabet $\{a,b,c,d\}.$

2. $w$ contains an even number of $a$'s

3. $w$ contains an even number of $b$'s.

For example, for $n=2$ there are $6$ such words: $aa, bb, cc, dd, cd, dc.$

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Source and history

task_id
420acef3-187f-52e3-a936-3ec14907f2e7
task_key
test--420acef3-187f-52e3-a936-3ec14907f2e7
task_revision_id
1
config / split
/ test

Official source

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