Probability and statistics question help?
Hi guys in currently taking a prob and stats class in university and one of my homework questions I cannot answer. So the question is: Suppose there's 5 men and 5 women applying for 5 ranked positions. 1 is best 5 is worst. How many different ways can one assign these candidates such that the first 3 ranks are taken by all men and the last 2 ranks are both women? I'm a little confused how to go about this as I know there's some permutation involved but... Idk
September 10, 2014
4 Comments • Newest first
Still tryna know why it's (5p3) (5p2) because I'm like fine with the fact that theres (5p3) ways to arrange the men in 3 ordered positions, same for 5p2 with the women. But couldn't the 3 positions be in the bottom for instance, with the 2 for the women on the top? how do we know that the men will get the top 3 positions?
EDIT: Hmmmm I think you guys are right, I was kinda overthinking it maybe? So there is absolutely nothing to do with cominations, its just soley permuation here. 5p3 works for any 3 positions, we just happen to choose the first, three. and 5p2 works for any two positions, we just choose the last two. I guess that makes sense..thanks guys
EDIT: But wait would it really be the same if the top two positions were held by females this time?
man A in rank 1, man B in rank 2 is not the same as man B in rank 1, man A in rank 2, so the order matters.
answer from 1st post seems right.
IDEK really, I'm confused because there's like a permutation part between groups of men and women themselves and then the order doesn't matter when it comes to the actual placement as long as there's 3 men / 2 women. Based on what you're saying, I should be doing (5x4x3) x (5x4)....
Isn't it (5 nPr 3)(5 nPr 2)?