A three-digit number is formed by selecting from the digits 1,2,3,4,5 and 6
with no repitition. How many of these three digit numbers will have a number
greater than 300?

Take a typical sample three-digit number, say:

                 523

We can choose the digit where the "5" is in 4 different ways, as 3,4,5, or 6.

Having chosen the first digit any of those 4 ways, that leaves 5 of the 6 that
weren't chosen as the first digit that can be chosen for the second digit,
where the "2" is in the sample.  So there are 4×5 or 20 ways to choose the
first two digits, to go where the "52" is.

Having chosen the first two digits any of those 4×5 or 20 ways, that leaves 4
of the original 6 that weren't chosen as either the first digit or the second
digit that can be chosen for the third digit, where the "3" is in the sample.
So there are 4×5×4 or 80 ways to choose the three digits. 

Here are the 80 ways listed:

1.  312
2.  314
3.  315
4.  316
5.  321
6.  324
7.  325
8.  326
9.  341
10.  342
11.  345
12.  346
13.  351
14.  352
15.  354
16.  356
17.  361
18.  362
19.  364
20.  365
21.  412
22.  413
23.  415
24.  416
25.  421
26.  423
27.  425
28.  426
29.  431
30.  432
31.  435
32.  436
33.  451
34.  452
35.  453
36.  456
37.  461
38.  462
39.  463
40.  465
41.  512
42.  513
43.  514
44.  516
45.  521
46.  523
47.  524
48.  526
49.  531
50.  532
51.  534
52.  536
53.  541
54.  542
55.  543
56.  546
57.  561
58.  562
59.  563
60.  564
61.  612
62.  613
63.  614
64.  615
65.  621
66.  623
67.  624
68.  625
69.  631
70.  632
71.  634
72.  635
73.  641
74.  642
75.  643
76.  645
77.  651
78.  652
79.  653
80.  654

Edwin