1
2, 1
3, 3, 1
4, 6, 4, 1
5, 10, 10, 5, 1
6, 15, 20, 15, 6, 1
7, 21, 35, 35, 21, 7, 1
8, 28, 56, 70, 56, 28, 8, 1
Write down the numbers 1, 2, 3, &c., as far as you please in a
column. On the right hand of 2 place 1, add them together and place
3 under the 1; the 3 added to 3 = 6, which place under the 3, and
so on; this gives the second column. The third is found from the
second in a similar way. By the triangle we can determine how many
combinations can be made, taking any number at a time out of a larger
number. For instance, a group of 8 gentlemen agreed that they should
visit the Crystal Palace 3 at a time, and that the visits should be
continued daily as long as a different three could be selected. In
how many days were the possible combinations of 3 out of 8 completed?
METHOD: Look down the first column till you come to 8, then
see what number is horizontal with it in the third column, viz., 56.
(For the method usually adopted for working out calculations like the
above, see DOCTRINE OF CHANCE.)