SOLUTION: A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?

Question 1097044: A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?
Found 3 solutions by jorel1380, greenestamps, MathTherapy:
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
12 choose 4=495
495 x 14=6930 different sub-committees possible
☺☺☺☺

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The first tutor who responded perhaps misread the problem. His answer is the number of ways that the committee can be formed with EXACTLY 4 senators, which means 1 of the 14 representatives:

But the problem says the committee must have AT LEAST 4 senators. So the earlier answer is missing the number of ways in which all 5 committee members are senators:

So the final answer to the problem is

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A certain congressional committee consists of 12 senators and 14 representatives. How many ways can a subcommittee of 5 be formed if at least 4 of the members must be senators?

Choosing 4 senators from 12 senators, times choosing 1 rep, from 14 reps., PLUS Choosing 5 senators from 12 senators, times choosing 0 reps, from 14 reps. This is: <======= Correct answer
RELATED QUESTIONS
A certain congressional committee consists of 9 senators and 11 representatives. How... (answered by Boreal)
A subcommittee of 5 representatives is to be selected from 10 men and 12 women members of (answered by ewatrrr)
There are 8 senators and 7 representatives. How many ways can a comittie of 6 be formed... (answered by stanbon)
A committee consists of 9 men and 14 women. In how many ways can a subcommittee of 3 men... (answered by jorel1380)
In how many ways can a chairperson and a vice chairperson be selected from a committee of (answered by Alan3354)
A five-member committee is to be selected from among four representatives of management... (answered by VFBundy)
How many ways can a 4-person subcommittee be selected from a committee of 9... (answered by Alan3354)
The executive committee of the student government consists of 10 members. In how many... (answered by Alwayscheerful)
in how many ways can a chairperson be selected from a committee of 38 senators (answered by stanbon)