Hi can anyone please explain me the first and the last question from today’s gregmat quant concept class?
If you know the basics of permutation and combination topic clearly then the solution is pretty straightforward. For the numerator you need to choose 4 students making sure there are equal number of freshman and junior students.
You can think like this.
F+J=Total
0+4=4
1+3=4
2+2=4
3+1=4
4+0=4
Among all these combinations the third one is correct since there are equal number of freshman and junior students.
Hi Rohit, thanks. I understand that in the numerator it should be 4C2*6C2 but could you explain the denominator? Why are we dividing?
Also do you have any suggestions on the last question?
Probability : \frac{\text{Number of Favorable/Desired outcome}}{\text{Number of possible outcome}}
Now, the total number of student are : 10, in which 6: Freshman and 4 : Junior
Now, the question asked 4 students to be selected randomly: Which means 10 \choose 4 and that is our Number of possible outcome
For our desired case is to have equal number of student from juniors and freshman :
\text{For Junior} : {4 \choose 2}
\text{For Freshman} : {6 \choose 2}
Equating everything:
Probablitiy = \frac{{4 \choose 2} \cdot {6 \choose 2}}{{10 \choose 4}}
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Its based on the concept of finding the factors, look at answer given by Bunnel in the link below:
https://gmatclub.com/forum/finding-number-of-factors-of-an-integer-question-163773.html