Aptitude Discussion

**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. |
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 |

**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.

${^ 5C_3} × {^{15}C_3} = 4,550$

**David**

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**Asmita**

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easy to understand!!!

!vry helpful 4 me.....

without any teachereasy to understand!!!!

**Ur Mum**

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Good one.

**Samar**

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

Good question!! Keep it up..:)