Permutation-Combination
Aptitude

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Common Information

There are $5$ freshmen, $8$ sophomores, and $7$ juniors in a chess club. A group of $6$ students will be chosen to compete in a competition.

Q.

Common Information Question: 1/4

How many combinations of students are possible if the group is to consist of exactly 3 freshmen?

 A.

5000

 B.

4550

 C.

4000

 D.

3550

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Solution:
Option(B) is correct

Here we need the number of possible combinations of 3 out of 5 freshmen,${^ 5C_3}$, and the number of possible combinations of 3 out of the 15 sophomores and juniors, ${^{15}C_3}$.

Note that we want 3 freshmen and 3 students from the other classes.

Therefore, we multiply the number of possible groups of 3 of the 5 freshmen times the number of possible groups of 3 of the 15 students from the other classes.

${^ 5C_3} × {^{15}C_3} = 4,550$


(4) Comment(s)


David
 ()

Good question!! Keep it up..:)



Asmita
 ()

easy to understand!!!

!vry helpful 4 me.....

without any teachereasy to understand!!!!



Ur Mum
 ()

Good one.



Samar
 ()

suggest alternative to the solution..it's still not clear to me..