MPMP: Can you play Scrabble over a video call?

From Standup Mathematician.

You can enter the submittable part of the puzzle at https://www.think-maths.co.uk/maths-puzzles

Everything about Vicki is on her website: https://www.vickipipe.co.uk/

Or go straight to the All The Stations channel!
https://www.youtube.com/channel/UC7ttKX46nJxUeXZ0aoD4Q5g

Get your own random quantum-noise numbers here: https://qrng.anu.edu.au/

These are my scrabble numbers. I have not double checked them, so please let me know if you do.

Ten million simulations:
Fixed points: 5.9604827
Alphabetical neighbours: 6.6008077
Pairs: 4.3016657
Triples: 0.2712588
Fours: 0.0184608
Fives: 0.0012537

Just two rounds of random shunting:
Fixed points: 5.9601175
Alphabetical neighbours: 5.6288508
Pairs: 6.263659
Triples: 0.4552404
Fours: 0.0385577
Fives: 0.0033718

Two random shunts and a 2-2-3-3 shuffle:
Fixed points: 5.9590569
Alphabetical neighbours: 7.2059461
Pairs: 4.2509397
Triples: 0.3174862
Fours: 0.0272161
Fives: 0.0023192

Three random shunts and a 2-2-3-3 shuffle:
Fixed points: 5.9611759
Alphabetical neighbours: 6.6348292
Pairs: 4.2771024
Triples: 0.2715075
Fours: 0.0184781
Fives: 0.0012264

Here is the submittable puzzle again with the letter values:

How many ways, from the 100 standard scrabble tiles, can you choose seven which total 46 points? Clarification: for this we mean distinct scrabble hands (groups of 7 letters), so order does not matter and identical letters are indistinguishable.

9 × A worth 1 point
2 × B worth 3 points
2 × C worth 3 points
4 × D worth 2 points
12 × E worth 1 point
2 × F worth 4 points
3 × G worth 2 points
2 × H worth 4 points
9 × I worth 1 point
1 × J worth 8 points
1 × K worth 5 points
4 × L worth 1 point
2 × M worth 3 points
6 × N worth 1 point
8 × O worth 1 point
2 × P worth 3 points
1 × Q worth 10 points
6 × R worth 1 point
4 × S worth 1 point
6 × T worth 1 point
4 × U worth 1 point
2 × V worth 4 points
2 × W worth 4 points
1 × X worth 8 points
2 × Y worth 4 points
1 × Z worth 10 points
2 × _ worth 0 points

Thanks as always to my principle channel sponsor Jane Street!

CORRECTIONS
– Nothing yet. Let me know if you spot anything!

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Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
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Ok, here is your hint: see if you can work out how many ways you can get a total of 48 points (there should be 50). Then try 46 points.