Print all the ways to aquire specific number using only specific numbers

Jelly, 10 bytes

ŒṗfƑƇL=¥Ƈ⁵

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A full program that takes the total, token values and number of arguments as its arguments. Returns a list of lists of token values.

Explanation

Œṗ          | Integer partition (of first argument)
    Ƈ       | Keep only those which:
   Ƒ        | - are invariant when:
  f         |   - filtered to only include the (implicit) second argument. 
       ¥Ƈ   | Keep only those for which:
     L      | - the length
      =  ⁵  |   - is equal to the third argument

J, ³⁵ 32 bytes

~.@((=1&#.)#])2+#&4/:~@#:[:i.4^]

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• Count in base 4 from 0 up to 4 ^ num_tokens to generate all the raw possibilities: #&4/:~@#:[:i.4^]
• Add 2 to all numbers so the tokens will have 2 3 4 5 labels instead of 0 1 2 3 labels: 2+
• Sort each possibility in preparation for removing dups: /:~@
• Filter the raw possibilities to include only those with the correct sum: ((=1&#.)#])
• Take the uniqs: ~.@

Perl 6, 64 bytes

{grep(*.sum==$_,|($/=2..5),|(+<<[\X] $/xx$_)[*;*])>>.Bag.unique}

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Fails for inputs above 7 due to Too many arguments in flattening array.This is because we are generating a list of every possible combination with repetition of numbers up to length n (where n is the same as the input), and not just that, but every possible ordering as well. Ah well, the price of being golfy...

This takes a number and returns a Bag, which is an unordered list of numbers and the amount in the bag.