Question

permutations and combinations

the board of directors at Belford community hospital has 12 members. three officers, president, vice president, and treasurer--must be elected from among the members. how many different slates of officers are possible?

a. do we use permutation rule or combination rule? what is the value of N, what is the value of R

b. use the permutation rule with n = 12 and r = 3 to compute P 12,3

Three members from the group of 12 on the board of directors at Belford community hospital will be selected to go to a convention (all expenses paid) in Hawaii. how many different groups of three are there?

c. do we use permutation rule or combination rule? what is the value of N, what is the value of R

d. use the permutation rule with n = 12 and r = 3 to compute C 12,3

Answer 1

Answer)

We use combination when the order is not important

And we use permutation when the order is important

1)

Here we need to select three officers president, vice president and treasurer from 12 members

So here specific order is important as rank is mentioned in the question

So we will use permutation

npr = n!/(n-r)!

12p3 = 12!/(12-3)! = 12*11*10*9!/9! = 1320

2)

Here we just need to choose three members from.the group of 12

Order is not important

So we will use combination

12c3 = 12!/(3!*(12-3)!)

= 220