There are 6 people on the board of supervisors for a homeowners' association. How many different 3-
person committees could be formed from the 6
people?

40 ways

Step-by-step explanation:

Step one:

given data

number of people= 6

number of committees=6

Required

The number of ways the committees can be formed differently

Step two:

Applying the combination formula we have

C(n,r)= n!/(n-r)r!

substitute

C(n,r)= 6!/(6-3)3!

C(n,r)= 6*5*4*3!/3*3!

C(n,r)= 6*5*4/3

C(n,r)= 120

/3

C(n,r)= 40 ways

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.