Question

The local high school football team, the Falcons, has a contest where three letters are chosen out of the seven letters F, A, L, C, O, N, and S and are printed in random order on tickets given one to each spectator. If anybody has the word "CAN" printed on their ticket, they win a free can of soda from the snack bar. What is the probability of winning a free soda?

Answer 1

well all of the letters are different, so that's good

Answer 2

so tell me how many total ways can you arrange those letter?

Answer 3

there are SEVEN letters
and they go in THREE slots

Answer 4

or your teacher might say there are seven letters and you choose THREE of them

Answer 5

do i need to do like the permutations ?

Answer 6

yes but without repetition

Answer 7

what you mean without repetition

Answer 8

nvm got it :p

Answer 9

FLS works because
\(\color{red}{F}\text A \color{red}{L}CON \color{red}{S}\)

Answer 10

but not FFL

Answer 11

you cannot use the F once it has already been used

Answer 12

is it 3/7

Answer 13

not quite

Answer 14

think about this
_ _ _

Answer 15

1/7

Answer 16

no just 7

Answer 17

why just 7 ?

Answer 18

seven different kinds of letters can go in the first position

Answer 19

F
A
L
C
O
N
S

Answer 20

what about when we choose our second letter? how many can we choose from?

Answer 21

remember we already used one of them

Answer 22

but it says winning the word "can"

Answer 23

i understand
"can" is just one word
but how many words are possible to get?

Answer 24

someone might get FLS
another person might get ACN
or SFA

Answer 25

right?

Answer 26

28 times you can arranged them

Answer 27

no

Answer 28

why not ?

Answer 29

because i can think of well over 28 ways to put them in

Answer 30

would you like to know how to find out?

Answer 31

yes because im lost

Answer 32

okay thats fine.
let me show you

Answer 33

see those three dashes? that is where we are going to put our letters

Answer 34

in the first one i am showing you that ANY of those seven letters can go as our first letter

Answer 35

so for our example choose a letter

Answer 36

f

Answer 37

okay now look what happened we just used the letter F and are left with
ALCONS

Answer 38

now you must choose our second letter

Answer 39

n

Answer 40

do you see?

Answer 41

yes