Question

Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?

Answer 1

You would use this formula

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

-----------------------------

Number of ways to choose 3 candidates = 10 C 3 = ??

Number of ways to choose 2 candidates = 10 C 2 = ??

Number of ways to choose 1 candidate = 10 C 1 = ??

Number of ways to choose 0 candidates = 10 C 0 = ??

Answer 2

A.

6 ways

B.

120 ways

C.

176 ways

D.

216 ways

Answer 3

have you seen that formula before?

Answer 4

yes

Answer 5

ok can you tell me what 10 C 3 equals?

Answer 6

ok

Answer 7

120

Answer 8

good, how about 10 C 2

Answer 9

6

Answer 10

no

Answer 11

try it again

Answer 12

176

Answer 13

do you have a calculator?

Answer 14

yea

Answer 15

what kind of calculator do you have?

Answer 16

ummm, its just the one on my computer

Answer 17

oh the windows calculator?

i see...that calculator won't do at all lol

one sec

Answer 18

ok here's a better way to do it

here is pascal's triangle

http://ptri1.tripod.com/ptreal1r.gif

do you see the row that starts with 1, 10, ... ?

Answer 19

ok
right

Answer 20

yeah

Answer 21

what's after the 10

Answer 22

5

Answer 23

look in row 10

Answer 24

row 10 has the numbers: 1, 10, ...

Answer 25

what's after the 10 in row 10 ?

Answer 26

1

Answer 27

to the right of 10

Answer 28

in row 10

Answer 29

45

Answer 30

good, what's after that

Answer 31

120

Answer 32

so this means


Number of ways to choose 3 candidates = 10 C 3 = 120

Number of ways to choose 2 candidates = 10 C 2 = 45

Number of ways to choose 1 candidate = 10 C 1 = 10

Number of ways to choose 0 candidates = 10 C 0 = 1


Add up all these ways: 120+45+10+1 = 176

Answer 33

So there are 176 ways to do this

Answer 34

ohhhhhhhh

Answer 35

hopefully it's making more sense now?