I can only try- Can you let me know how to align columns?
Let me try this again.
# => Number of Hearts left in the deck.
# of ways => Number of way that that amount of Hearts can be chosen from the 32 that are removed.
Prob => Probability of picking a Heart from the 20 left.
(This is done using Excel)
# # of ways Prob. # of ways * Probability
0 15,380,937 0.65 0.0000000793494867
1 799,808,724 0.6 0.0000038087753615
2 16,529,380,296 0.55 0.0000721551332366
3 181,823,183,256 0.5 0.0007215513323662
4 1,198,380,071,460 0.45 0.0042801113124451
5 5,033,196,300,132 0.4 0.0159790822331284
6 13,938,082,061,904 0.35 0.0387185454110420
7 25,885,009,543,536 0.3 0.0616336028992096
8 32,356,261,929,420 0.25 0.0642016696866767
9 26,963,551,607,850 0.2 0.0428011131244512
10 14,592,039,693,660 0.15 0.0173722165034537
11 4,864,013,231,220 0.1 0.0038604925563231
12 896,002,437,330 0.05 0.0003555716828192
13 68,923,264,410 0 –
Total 125,994,627,894,135 0.2500000000000000
Here are the formulas used: (Starting from Cell A1)
# # of ways Prob. # of ways * Probability
0 =COMBIN(13,13-A2)*COMBIN(39,7+A2) =(13-A2)/20 =(B2/$B$16)*C2
1 =COMBIN(13,13-A3)*COMBIN(39,7+A3) =(13-A3)/20 =(B3/$B$16)*C3
2 =COMBIN(13,13-A4)*COMBIN(39,7+A4) =(13-A4)/20 =(B4/$B$16)*C4
3 =COMBIN(13,13-A5)*COMBIN(39,7+A5) =(13-A5)/20 =(B5/$B$16)*C5
4 =COMBIN(13,13-A6)*COMBIN(39,7+A6) =(13-A6)/20 =(B6/$B$16)*C6
5 =COMBIN(13,13-A7)*COMBIN(39,7+A7) =(13-A7)/20 =(B7/$B$16)*C7
6 =COMBIN(13,13-A8)*COMBIN(39,7+A8) =(13-A8)/20 =(B8/$B$16)*C8
7 =COMBIN(13,13-A9)*COMBIN(39,7+A9) =(13-A9)/20 =(B9/$B$16)*C9
8 =COMBIN(13,13-A10)*COMBIN(39,7+A10) =(13-A10)/20 =(B10/$B$16)*C10
9 =COMBIN(13,13-A11)*COMBIN(39,7+A11) =(13-A11)/20 =(B11/$B$16)*C11
10 =COMBIN(13,13-A12)*COMBIN(39,7+A12) =(13-A12)/20 =(B12/$B$16)*C12
11 =COMBIN(13,13-A13)*COMBIN(39,7+A13) =(13-A13)/20 =(B13/$B$16)*C13
12 =COMBIN(13,13-A14)*COMBIN(39,7+A14) =(13-A14)/20 =(B14/$B$16)*C14
13 =COMBIN(13,13-A15)*COMBIN(39,7+A15) =(13-A15)/20 =(B15/$B$16)*C15
14 =SUM(B2:B15) =SUM(D2:D15)