How many ways are there to select a subcommittee of 7 members from among a committte of 17?

Answer 1

The first member can be any one of 17 people. For each one . . .

The second member can be any one of the remaining 16 people. For each one . . .

The third member can be any one of the remaining 15 people. For each one . . .

The fourth member can be any one of the remaining 14 people. For each one . . .

The fifth member can be any one of the remaining 13 people. For each one . . .

The sixth member can be any one of the remaining 12 people. For each one . . .

The seventh member can be any one of the remaining 11 people.

Total number of ways to pick 7 people from the 17 =

(17 x 16 x 15 x 14 x 13 x 12 x 11) = 98,017,920 ways.

But that's not a useful answer. Not all of the 98 million ways produce different

subcommittees. There are a lot of different ways to pick the same 7 people and

wind up with the same group of seven.

Number of ways to select (or seat) the same 7 people = (7 x 6 x 5 x 4 x 3 x 2) = 5,040 ways.

So, among the 98 million different ways of selecting 7 people, each unique group

will show up 5,040 times.

The number of different, unique 7-member subcommittees that can be selected from

among 17 people is

98,017,920 / 5,040 = 19,448 .