Heres a probability question.
There are 3 Republicans and 2 Democrats on a Senate committee. If a 3 person subcomittee is to be formed from this committee, what is the probability of selecting 2 Republicans and 1 Democrat?
I know that no. of ways to select 2 Rep. is 3, and that no. of ways to select 1 Dem. is 2 for 6 (3 x 2) possible ways. But how do you determine the total number of ways?(6/?)
What is the least interger greater than 999 that is divisible by 6, 8, 9?
I was able to do this question fairly quickly by trial and error but was wandering if there is perhaps a mathematical and more direct approach. (maybe prime factorization)
Use prime factorization. 6 is 2*3, 8 is 2^3, and 9 is 3^2. The find the LCM, just choose the highest power of each factor. This gives you (2^3)*(3^2) = 8*9 = 72. Thus the number must be a multiple of 72. It is simple to see that the first multiple of 72 greater than 999 is 1008.
difficult set question: a study of 400 fruit orchards showed that 250 of the orchards grew apples, 140 grew pears, 95 grew plums, 70 grew only apples and pears, 30 grew only apples and plums, 45 grew only pears and plums, and 10 grew all three.
18. how many of the orchards grew only apples or plums?
a) 30
b) 130
c) 150
d) 180
e) 345
19. How many of the orchards grew no apples, pears, or plums?
a) 0
b) 80
c) 165
d) 235
e) 320
18. the answer is a
19. I think the answer should be 50 but I dont see it as a choice?
The easiest way to solve this is to make a venn diagram with three circles. Start with the last piece of information and work your way back while filling in your chart. I'm not sure why I'm not getting an answer choice for q 19. Maybe there is a mistake.
@ Arachnotron
this is related to GRE's question about rate and time. I figured out the rates but can you explain why you did this : (27sec/90ft)(100ft) = 30 seconds.?
oops I was writing while you posted it.
Here is my explanation: first make 3 overlapping circles labeled apples, pears, and plums
fill out the venn diagram as follows
1. the place where the 3 circles intersect will be 10
2. the place where only apples and plums intersect will be 30
3. the place where only pears and plums intersect will be 45
4. the place where only apples and pears intersect will be 70
5. remaining apples will be 250-30-10-70=140
6. remaining pears will be 140-70-10-45=15
7. remaining plums will be 95-30-10-45=10
18. only apples or only plums is 140+10=150
19. to see how many are none use 400-140-30-70-10-15-45-10=80
In the BB, there is this example question concerning combinations:
There are 12 students in the school theater class. Two students will be responsible for finding the props needed for the skit the class is performing. How many different pairs of students can be chosen to find the props?
- To get the answer, you first multiply 12 by 11 to get the number of ways of choosing a pair of students, and then you divide by 2 because each pair of students can be chosen in two different ways. The answer is 66.
I do not understand why we have to divide by 2 because each pair of students can be chosen in two different ways. I thought in combinations, the order doesn't matter, so we shouldn't have to worry about this. And why are we dividing? I am confused.
You multiply 12 by 11 to find the number of groups of 2 out of 12 people. For the first person, there are 12 possibilities, and for the second person, there are 11 possibilities. (You can't have a person be the first and second choices.) Therefore you must multiply 12 by 11.
Next, you have to divide by 2. From what I did before, each pair of students can be chosen in two different ways. For example, student A and student B can be chosen as A then B, or B then A. To get rid of these extra pairs, we divide our answer from the first step by 2.
Replies to: Math help center
There are 3 Republicans and 2 Democrats on a Senate committee. If a 3 person subcomittee is to be formed from this committee, what is the probability of selecting 2 Republicans and 1 Democrat?
I know that no. of ways to select 2 Rep. is 3, and that no. of ways to select 1 Dem. is 2 for 6 (3 x 2) possible ways. But how do you determine the total number of ways?(6/?)
factor out A^6 from numerator: A^6(A-1)/(A-1)
then divide out (A-1)
I was able to do this question fairly quickly by trial and error but was wandering if there is perhaps a mathematical and more direct approach. (maybe prime factorization)
18. how many of the orchards grew only apples or plums?
a) 30
b) 130
c) 150
d) 180
e) 345
19. How many of the orchards grew no apples, pears, or plums?
a) 0
b) 80
c) 165
d) 235
e) 320
19. I think the answer should be 50 but I dont see it as a choice?
The easiest way to solve this is to make a venn diagram with three circles. Start with the last piece of information and work your way back while filling in your chart. I'm not sure why I'm not getting an answer choice for q 19. Maybe there is a mistake.
apples + plums
this is related to GRE's question about rate and time. I figured out the rates but can you explain why you did this : (27sec/90ft)(100ft) = 30 seconds.?
19. the answer is b) 80. @altamash why did you switch answers
Here is my explanation: first make 3 overlapping circles labeled apples, pears, and plums
fill out the venn diagram as follows
1. the place where the 3 circles intersect will be 10
2. the place where only apples and plums intersect will be 30
3. the place where only pears and plums intersect will be 45
4. the place where only apples and pears intersect will be 70
5. remaining apples will be 250-30-10-70=140
6. remaining pears will be 140-70-10-45=15
7. remaining plums will be 95-30-10-45=10
18. only apples or only plums is 140+10=150
19. to see how many are none use 400-140-30-70-10-15-45-10=80
There are 12 students in the school theater class. Two students will be responsible for finding the props needed for the skit the class is performing. How many different pairs of students can be chosen to find the props?
- To get the answer, you first multiply 12 by 11 to get the number of ways of choosing a pair of students, and then you divide by 2 because each pair of students can be chosen in two different ways. The answer is 66.
I do not understand why we have to divide by 2 because each pair of students can be chosen in two different ways. I thought in combinations, the order doesn't matter, so we shouldn't have to worry about this. And why are we dividing? I am confused.
Next, you have to divide by 2. From what I did before, each pair of students can be chosen in two different ways. For example, student A and student B can be chosen as A then B, or B then A. To get rid of these extra pairs, we divide our answer from the first step by 2.