Lesson 6: Prob #9- what is n and k
For 6.9 I am confused as to where the numbers come from for Set B as far as C(16,5). For Set A n= 17 because you do not include the other 2 triplets and the other twin and k=7 because every person would be different, is this thought process correct? But for Set B n=16 because you can have either twin 1 or 2 show up and either (triplet 1, triplet 2) , (triplet 1,3) , or (triplet 2, triplet 3) show up, and k= 5 because you have already selected 2 of the 7 (one twin, one triplet)? Is this correct?
ShivaniGillon: Jan. 28, 2015, 10:28 a.m.
For Set B, you would exclude all 3 triplets from n because you know that you have to have exactly 2 triplets and, by that logic, you know you cannot pick a third triplet. With regards to the twins, you can exclude 1 of the 2 twins from n because in Set B, you state that you can have at most only 1 twin. Therefore, your n would be 20-3-1=16. Your k=5 because you known you have already chosen 2 triplets (You cannot say you picked one twin because the set states that at most 1 twin can be chosen, which includes the possibility that no twin is chosen).
weisbart: Feb. 1, 2015, 11:06 a.m.
Perfect ShivaniGillon! Nice explanation.