word question

Question

in how many ways can a subcommittee of four be chosen from a Senate committee of five Democrats and four Republicans if   (a) All members are eligible?   (b)  The subcommittee must consist of two republicans and two Democrats?  Show me how?

Answer 1

I believe the answer to a) is 126 and to b) is 60 based on the wording or your problem that order does not seem to matter and that we are dealing with combinations.

 

Combination formula is: n! divided by (n-r)! times r! where n = total objects, r = selected objects needed, and ! means factorial.

 

For a):  9!/(9-4)! times 4! = 9*8*7*6*5!/5!*4! = 3024/24 (cancel 5! top and bottom) = 126

 

For b) the explanation first is : In this case you must select 2 republicans from 4 and also 2 democrats from 5.  Since and is used you must multiply the results of the two combinations together to get your final answer. 

 

So for b): 4!/(4-2)!*2!  times  5!/(5-2)!*2 = 4*3*2!/2!*2! times 5*4*3!/3!*2! = 12/2 times 20/2 = 6 times 10 = 60

 

Hope this helps. :)