Question

HELP WITH PROBABILITY!
A quiz has ten true/false questions. In how many different ways can a student get exactly 70% on the quiz?

Answer 1

70%

Answer 2

The answer isn't 70%

Answer 3

It's basically asking how many ways are there to get 7 questions right

or how many ways to get 3 questions wrong

Answer 4

yeah how many ways?

Answer 5

to find out how many ways, you need to compute 10 C 3

so you use the formula

n C r = (n!)/(r!*(n-r)!)

Answer 6

why is it 10C3

Answer 7

there are 10 problems to chose from

there are 3 slots to fill in (call these slots "wrong answers")

Answer 8

wouldnt it be 10C7 if anything

Answer 9

10 C 7 = 10 C 3

Answer 10

due to symmetry (think of pascals triangle)

Answer 11

ok so it would be 120?

Answer 12

correct

Answer 13

thank you

Answer 14

can you help me with another one

Answer 15

sure

Answer 16

The US Senate has two senators from each of 50 states. In how many ways can a committee of five senators be chosen if no state is to have two members on the committee?

Answer 17

hmm let me think, my initial thought was off

Answer 18

ok

Answer 19

I'm still trying, but I'm trying with a much smaller set

this is so I can confirm my answer, one sec

Answer 20

ok thank you

Answer 21

well so far, I've managed to use a smaller set of 10 states (20 senators total)

I count 8064, but I'm not sure how to extend it to 50 states (100 senators total)

Answer 22

ok thank you! i can try to ask my teacher tomorrow but thank you for you help i think i see how it would start to work out

Answer 23

I'll think on it a bit later, maybe I'm just going at it the wrong way

Answer 24

alright

Answer 25

usually a break clears the head and makes me try it a whole different way

but yeah that's a good idea