Table of Contents

Some counting problems and estimates

Committees of five people from the United States Supreme Court.

Number the justices 1, 2, 3, 4, 5, 6, 7, 8, 9. One committee consists of Justices 1, 2, 3, 4, and 5. Write that committee as 12345. Another committee is 13579.

Here they all are (maybe):

12345 12346 12347 12348 12349
12356 12357 12358 12359 12367
12368 12369 12378 12379 12389
12456 12457 12458 12459 12467
12468 12469 12478 12479 12489
12567 12568 12569 12578 12579
12589 12678 12679 12689 12789

13456 13457 13458 13459 13467
13468 13469 13478 13479 13489
13567 13568 13569 13578 13579
13589 13678 13679 13689 13789

14567 14568 14569 14578 14579
14589 14678 14679 14689 14789
15678 15679 15689 15789 16789

23456 23457 23458 23459 23467
23468 23469 23478 23479 23489
23567 23567 23569 23578 23579
23589 23678 23679 23689 23789

24567 24568 24569 24578 24579
24589 24678 24679 24689 24789
25678 25679 25689 25789 26789

34567 34568 34569 34578 34579
34589 34678 34679 34689 34789
35678 35679 35689 35789 36789

45678 45679 45689 45789 46789
56789

Count them (how?). There appear to be 126. Did we miss any? Did we list any of them twice?