How many different 4 member communities can be formed from a group of 15 people?
a. 1120
b. 1365
c. 966
d. 925

The first member can be any one of the 15 people.
       For each of those . . .
The second member can be any one of the remaining 14 people.
       For each of those . . .
The third member can be any one of the remaining 13 people.
       For each of those . . .
The fourth member can be any one of the remaining 12 people.

The number of ways to make a 4-member group is . . .

               (15 x 14 x 13 x 12)  =  32,760 ways.

BUT . . .  there aren't that many DIFFERENT GROUPS.

Each 4-member group can be arranged in  (4 x 3 x 2 x 1) = 24 different orders.
All those possible orders show up in the  32,760 number.
Each different group gets counted 24 times in that number, in all its possible orders.

The number of DIFFERENT 4-member GROUPS that can be formed
from the 15 people is

                                 (32,760) / (24)  =  1,365 different groups.

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