A school dance committee of four people is selected at random from a group of 9 ninth graders, 8 eighth graders, and 10 seventh graders. What is the probability that the committee has all seventh graders? The probability that the committee has all seventh graders is?

Question

NOTE: I realize that this is a combination problem with 10C4 as the set up. But my question is how would I go about multiplying and dividing this out into a fraction? I am a new learner to permutations and combinations.

Answer 1

how many 4 person committees can be selected from the 27 students
... 27C4

how many 4 person committees can be selected from the 10 7th graders
... 10C4

probability of all 7th graders ... 10C4 / 27C4