Information about a new found fact !

[Commander]

New Invention about Bridge Hands Distribution !

In the Card Game of Bridge 13 cards out of 52 are dealt to a Player.

They contain Suits Spades, Hearts, Diamonds or Clubs and each suit may have 0 – 13 cards with all Suits adding to 13 cards in the hand !

We tried to evaluate the total number of Combinations possible and found that the number is 560 !

Varying the numbers from 0 – 13 as the left most number of the Combination [say Spades holding] we got following :

I give here the summary : number of combinations with the first spot [Spades] having 0,1,2,...,12,13 & the Cumulative total in the last Column !

0	105	105
1	91	196
2	78	274
3	66	340
4	55	395
5	45	440
6	36	476
7	28	504
8	21	525
9	15	540
10	10	550
11	6	556
12	3	559
13	1	560

Interestingly 560 is a great number which is the Sum of the first 14 Triangular Numbers !

1+3+6+10+15+21+28+36+45+55+66+78+91+105 = 560

That is :

   1

+ 1+2

+ 1+2+3

+ 1+2+3+4

+ 1+2+3+4+5

+ 1+2+3+4+5+6

+ 1+2+4+4+5+6+7

+ 1+2+3+4+5+6+7+8

+ 1+2+3+4+5+6+7+8+9

+ 1+2+3+4+5++6+7+8+9+10

+ 1+2+3+4++5+6+7+8+9+10+11

+ 1+2+3+4+5+6+7+8+9+10+11+12

+ 1+2+3+4+5+6+7+8+9+10+11+12+13

+ 1+2+3+4+5+6+7+8+9+10+11+12+13+14

= 560

What a number !

You can call 560 a DOUBLE TRIANGULAR NUMBER  !