Holdkammeraten vælger bowlingskoene og en blå bowlingkugle.

In Danish, the definite article is often attached to the end of the noun instead of standing as a separate word.

• holdkammerat = teammate
• holdkammeraten = the teammate

So -en here means the.

This noun is a common gender noun, which is why it takes -en in the singular definite form.

Because Danish usually expresses the by adding an ending to the noun:

• en holdkammerat = a teammate
• holdkammeraten = the teammate

Unlike English, Danish does not normally say a separate the in this kind of sentence. The definiteness is built into the noun itself.

Danish likes compound nouns, much more than English does.

So what English writes as bowling shoes is naturally written as one word in Danish:

• bowlingsko = bowling shoe / bowling shoes as a compound base
• bowlingskoene = the bowling shoes

This is very normal in Danish. The same thing happens with:

• bowlingkugle = bowling ball
• fodboldhold = football team
• sommerferie = summer holiday

The ending -ene is a common way to make a noun plural definite in Danish.

So:

• en bowlingsko = a bowling shoe
• bowlingsko = bowling shoes
• bowlingskoene = the bowling shoes

Here it shows both:

• plural = more than one shoe
• definite = the shoes

Because bowlingkugle is a common gender noun, not a neuter noun.

In Danish, adjectives change depending on the noun:

• with a common gender singular indefinite noun: blå
• with a neuter singular indefinite noun: usually blåt
• with plural or definite forms: often blå

So here:

• en blå bowlingkugle = a blue bowling ball

If the noun were neuter, you would expect something like et blåt ...

Because it is modifying a singular indefinite common gender noun:

• en blå bowlingkugle

That is the basic form of the adjective in this situation.

Compare:

• en blå kugle = a blue ball
• et blåt hus = a blue house
• de blå kugler = the blue balls

So blå is correct because kugle takes en, not et.

Because the two noun phrases are different:

• bowlingskoene is already definite plural: the bowling shoes
• en blå bowlingkugle is indefinite singular: a blue bowling ball

So:

• -ene on bowlingskoene already includes the idea of the
• en is needed before blå bowlingkugle because that noun phrase is indefinite

This mix is completely normal:

• the bowling shoes
  • a blue bowling ball

Vælger is the present tense of vælge, which means to choose.

Danish present tense is often made by adding -r to the infinitive:

• at vælge = to choose
• vælger = chooses / is choosing

So:

• Holdkammeraten vælger ... = The teammate chooses ...

Danish present tense can often cover both English chooses and is choosing, depending on context.

Yes. This is very standard Danish word order:

• Holdkammeraten = subject
• vælger = verb
• bowlingskoene og en blå bowlingkugle = object

So it follows the familiar pattern:

Subject + Verb + Object

That makes this sentence straightforward for an English speaker.

Yes, absolutely.

Here the sentence joins:

• bowlingskoene = the bowling shoes
• en blå bowlingkugle = a blue bowling ball

with og = and

There is nothing unusual about that. Danish can coordinate noun phrases even when they differ in:

• definiteness
• number
• article use

English does exactly the same:

• the shoes and a blue ball

Yes.

• bowling
  • kugle = bowlingkugle

Literally, this is bowling-ball as one written word. Danish strongly prefers compounds to be written together, where English often writes separate words.

So both of these are compounds:

• bowlingskoene
• bowlingkugle

You have to learn the gender of each noun.

In Danish, singular nouns are mainly either:

• common gender → take en
• neuter → take et

In this sentence:

• en holdkammerat
• en bowlingkugle
• en bowlingsko

All of these are common gender nouns.

Unfortunately, gender is not always predictable, so it is best to learn a new noun together with its article:

• en kugle
• en sko
• en holdkammerat

Then the noun phrase would become definite, and Danish would normally use the double definite pattern with an adjective:

• den blå bowlingkugle = the blue bowling ball

So the full sentence would be:

• Holdkammeraten vælger bowlingskoene og den blå bowlingkugle.

This is different from the indefinite version:

• en blå bowlingkugle = a blue bowling ball

That is an important pattern in Danish:

• en blå kugle = a blue ball
• den blå kugle = the blue ball