SOLUTION: A group of three seniors, six juniors, and five sophomores must select a committee of three. How many committees are possible if the committee must contain the following: a. One

Algebra.Com
Question 322422: A group of three seniors, six juniors, and five sophomores must select a committee of three. How many committees are possible if the committee must contain the following:
a. One person from each class.
b. Any mixture of the classes.
c. Exactly two seniors.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A group of three seniors, six juniors, and five sophomores must select a committee of three. How many committees are possible if the committee must contain the following:
a. One person from each class.
# of ways = 3*6*5 = 90
-----------------------------
b. Any mixture of the classes.
14C3 = 364
-----------------------------
c. Exactly two seniors.
3C2*11 = 3*11 = 33
=======================
Cheers,
Stan H.
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
A group of three seniors, six juniors, and five sophomores must select a committee of three. How many committees are possible if the committee must contain the following:
a. One person from each class.

Choose the senior 3 ways, then choose the junior 6 ways, 
then choose the sophomore 5 ways.  3x6x5 = 90 possible 
committees.

b. Any mixture of the classes.

14 students, choose 3 = 14C3 =

c. Exactly two seniors.

(3 seniors, choose 2) AND (11 non-seniors choose 1) = (3C2)(11C1) = = 3*11 = 33 ways.

Edwin
RELATED QUESTIONS

A group of three seniors, six juniors, and five sophomores must select a committee of... (answered by Alan3354)
A group of three seniors, six juniors, and five sophomores must select a committee of... (answered by jim_thompson5910)
A group of eleven seniors, nine juniors, five sophomores, and four freshmen must select a (answered by Boreal)
A committee of 10, consisting of 1 freshman, 2 sophomores, 4 juniors, and 3 seniors is to (answered by Edwin McCravy)
A committee of 16 students is chosen from eight juniors and eight seniors. A. How many (answered by ewatrrr)
A class has nine sophomores, three juniors, and six seniors. In how many different ways... (answered by Boreal)
A five member committee is being formed from group of 9 sophomores and 12 seniors. How... (answered by ewatrrr)
Finite mathematics- Miss Anderson wants to select a committee of five people from her (answered by VFBundy)
There are six seniors four juniors and two sophomores. If a committee of three is to... (answered by stanbon)