SOLUTION: Please help me solve this equation 1.Give your answer the following three questions in symbolic form, using the notation. a. the board of directors of a company has 14 members.

Algebra ->  Permutations -> SOLUTION: Please help me solve this equation 1.Give your answer the following three questions in symbolic form, using the notation. a. the board of directors of a company has 14 members.      Log On


   

Question 892184: Please help me solve this equation
1.Give your answer the following three questions in symbolic form, using the notation.
a. the board of directors of a company has 14 members. in how many ways can it choose a committee of three members? (where all members have equal standing)
b. 22 drivers start a race. assuming all of the drivers are equally skilled. how many top five finishes are possible?
c. how many different 3 topping pizzas can be made from a list of 20 different toppings?
Thank you =)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
C is for Combination and also for CHOOSE.
P is for Permutation and also for PLACE and POSITION.

If you just CHOOSe things you don't care what order you choose them in.  

But when you PLACE things in a certain POSITION what order you PLACE or 
POSITION them in IS important.

1.Give your answer the following three questions in symbolic form, using the notation. 
a. the board of directors of a company has 14 members. in how many ways can it choose a committee of three members? (where all members have equal standing)

We're just Choosing here, and we don't care what order we choose them in.

So that's 

14 members CHOOSE 3.  

There are several different notations used for that, depending on your book
and/or teacher.  They are

C(14,3), 14C3, 14C3, and %28matrix%282%2C1%2C14%2C3%29%29.

Use the one your teacher uses.

b. 22 drivers start a race. assuming all of the drivers are equally skilled. how many top five finishes are possible?
Here the 5 drivers are PLACED in a certain order.  There is the one in 1st
PLACE, 2nd PLACE, third PLACE, 4th PLACE, and 5th PLACE.  So order is important,
so we have

22 drivers PLACE 5.

That's either written P(23,5), 23P5, or 23P5.

c. how many different 3 topping pizzas can be made from a list of 20 different toppings?
We're just Choosing, not POSITIONING or PLACING, (because we don't care if
the mushrooms are above or below the black olives or vice-versa).

20 toppings choose 3 = C(20,3), 20C3, 20C3, or %28matrix%282%2C1%2C20%2C3%29%29 

Edwin