A rajtszám a táskámban van.

Because a is the Hungarian definite article, meaning the.

So:

• a rajtszám = the race number / the bib number
• a táskámban = in my bag

Hungarian uses the definite article in places where English would also usually use the.

A small note: Hungarian has two forms of the:

• a before most consonants
• az before vowels

For example:

• a táska = the bag
• az autó = the car

Hungarian often builds meanings into one word by adding suffixes.

táskámban breaks down like this:

• táska = bag
• -m = my
• -ban = in

So:

• táska → bag
• táskám → my bag
• táskámban → in my bag

This is very normal in Hungarian. Instead of using separate words like in my bag, Hungarian attaches the possessive ending and the case ending directly to the noun.

Because Hungarian often inserts a linking vowel before possessive endings.

Here the possessive form is:

• táska
  • -m → táskám

That long á is part of how the word sounds in the possessed form. This is something learners usually have to get used to word by word and pattern by pattern.

Other examples:

• autó → autóm = my car
• könyv → könyvem = my book
• ház → házam = my house

So the possessive ending is not always added in a perfectly mechanical way; the shape of the noun may change slightly.

Both -ban and -ben mean in, but Hungarian chooses between them by vowel harmony.

• -ban is used with back-vowel words
• -ben is used with front-vowel words

Since táska has back vowels, it takes -ban:

• táskában = in the bag
• táskámban = in my bag

Compare:

• székben = in the chair
• kertben = in the garden

So -ban/-ben are the same case ending; the choice depends on the vowels in the word.

That is a very common and important question.

Hungarian usually omits van in simple present-tense sentences of the type X is Y:

• A táska nagy. = The bag is big.
• Ő tanár. = He/She is a teacher.

But van is normally used when you say that something is somewhere, or exists somewhere:

• A táska az asztalon van. = The bag is on the table.
• A rajtszám a táskámban van. = The race number is in my bag.

So in location sentences, van usually stays.

Rajtszám literally means something like start number.

It is commonly used for:

• a race bib number
• a competition number
• a starting number worn by a runner or athlete

It is a compound noun:

• rajt = start
• szám = number

So even though English may say race number or bib number, Hungarian uses this single compound word.

Yes, Hungarian word order is flexible, but different orders change the focus or emphasis.

This version is a neutral sentence:

• A rajtszám a táskámban van.

It presents the race number as the topic, then says where it is.

Other orders are possible:

• A táskámban van a rajtszám.
  This can sound more like It’s in my bag that the race number is / The race number is in my bag with more focus on the location.

Hungarian word order is not random. It often reflects:

• what the sentence is about
• what is new information
• what is emphasized

So the sentence you have is a very natural, standard way to say it.

This is one of the most important location contrasts in Hungarian.

• -ban/-ben = in something, already inside, no movement
• -ba/-be = into something, movement toward the inside

So:

• A rajtszám a táskámban van. = The race number is in my bag.
• Beteszem a rajtszámot a táskámba. = I put the race number into my bag.

English learners often mix these up, because English sometimes uses in for both location and movement in casual speech, but Hungarian keeps them separate much more clearly.

Because Hungarian usually expresses possession with an ending on the noun, not a separate possessive word like English my.

So:

• táska = bag
• táskám = my bag
• táskád = your bag
• táskája = his/her bag

This is one of the biggest structural differences from English. Instead of saying something like my bag with two separate words, Hungarian often says it with one word.

You would use egy, which means a/an.

For example:

• A rajtszám egy táskában van. = The race number is in a bag.

But notice the meaning difference:

• a táskámban = in my bag
• egy táskában = in a bag

You normally would not say egy táskámban, because my bag is already specific and definite.

A simple approximation for an English speaker is:

• A = short aw
• rajt ≈ right
• szám ≈ saam with a long aa
• a = again short aw
• táskámban ≈ taash-kaam-bawn
• van = vawn

A few useful pronunciation notes:

• sz is pronounced like English s
• s by itself is pronounced like English sh
• á is a long vowel, somewhat like a in father
• stress is always on the first syllable:
  RAJTszám, TÁSkámban

So the stress pattern is:

A RAJTszám a TÁSkámban van.