MPMP: Can you play Scrabble over a video call?

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

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

Or go straight to the All The Stations channel!
   / @allthestations  

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!

Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:

Bevan Timm
Steve Davidson
Aimee Arost Henry Gustafson
Emily Dingwell
Matt Langford
Mikko
Daniel DeJarnatt
Alex Frieder
Will Clark
Daniel Brockwell

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Filming and editing by Matt Parker
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.