Question

How Many three digit numbers can be written using no 0's and at least one 7

answer is 217 but why?

Answer 1

possibilities are
xx7
x7x
7xx
777
77x
7x7
x77

where x = 1-6, 8 or 9

Answer 2

(# ways to have 3digit number with no zeros)-(#ways to have 3 digit number with no zeros or sevens)

Answer 3

ahhh - yes

Answer 4

cwrw238's way will also work

Answer 5

@AlexBabich is repetition allowed

Answer 6

no every number can only be used once

Answer 7

if it is 'at least one 7' then I'd say repetition is allowed

Answer 8

otherwise it would say you have to use a 7

Answer 9

yes

Answer 10

also...with repetition you get the answer given in the OP

Answer 11

what do you mean by repitition?

Answer 12

777 is a possibility...557 is a possibility...ect

Answer 13

ahh yea of course, I thought it was meant repeating the same number

Answer 14

for xx7, number of xx's will be 8P2 + 8 right?

Answer 15

no just 8*8

Answer 16

8P2 + 8 =8*8

Answer 17

what does 8p2 mean, its not 8 power 2?

Answer 18

8P2=8*7

Answer 19

number of permutations of 2 in 8 = 8*7

Answer 20

\[_nP_r=\frac{n!}{(n-r)!}\]

Answer 21

so i guess that would be 64 ways for x7x and 7xx

total * 64 = 192

Answer 22

and the others are 1 + 8 + 8 + 8 = 25

Answer 23

yea i added up all the ways you gave me and got 217, but i didnt use permutations, I havent even learned that, i just did 8*8 for the ones with 2 spaces added them up and did...what you just typed is what i did

Answer 24

9*9*9-8*8*8

Answer 25

- that IS an easier way!!

Answer 26

@Zarkon yes i did the way you said and got the same result

Answer 27

Thank you both so much! :)

Answer 28

yw