Scrabble Puzzle (MPMP Puzzle 3)

Submission is now closed. Go back to main page for live puzzle.

Please note: The solution video for this one will take longer than normal. It will not be out on Friday 17th April. 

The puzzle for submission:  'How many ways, from the 100 standard scrabble tiles, can you choose seven which total 46 points?' Clarification: for this we're asking you how many distinct scrabble hands (groups of 7 letters) there are that total exactly 46. So order does not matter and identical letters are indistinguishable

The distribution of scrabble tiles and points is below. (Eg the letter A is worth 1 point, and there are 9 letter A tiles)

0 points - blank (x2)

1 point - A (x9), E (x12), I (x9), O (x8), U (x4), L (x4), N (x6), S (x4), T (x6), R (x6)

2 points -D (x4), G (x3)

3 points -B (x2), C (x2), M (x2), P (x2)

4 points -F (x2), H (x2), V (x2), W (x2), Y (x2)

5 points -K (x1)

8 points - J (x1), X (x1)

10 points -Q (x1), Z (x1)