Question

a 3 digit number is formed from the odd digits 1,3,5,7,9. numbers can only be used once how many numbers are larger than 350

Answer 1

_ _ _

left most space can be chosen from {3, 5, 7, 9} = 4 ways
next space can be chosen from {5, 7, 9}-1 = 2 ways
last spce canbe chosen from {1, 3, 5, 7, 9}-2 = 3 ways

total numbers larger than 350 = 4*2*3

Answer 2

howcome answer is 4*3*3? what to do with the 1st and 2nd digit when theres overlap in set solutions??

Answer 3

wait.. i see something wrong ... gimme some time

Answer 4

pls scratch previous stuff..
see if below makes sense :

case I : first digit = 3
second digit can be chosen from {5, 7, 9} = 3 ways
last digit can be chosen from {1, 3, 5, 7, 9} -2 = 3 ways

total number of ways = 3*3 = 9

case II : first digit can be one of { 5, 7, 9} = 3 ways
second digit can be chosen from {5, 7, 9} -1 = 2 ways
last digit can be chosen from {1, 3, 5, 7, 9} -2 = 3 ways

total number of ways = 3*2*3 = 18

total numbers larger than 350 = 9 + 18

Answer 5

yeah i tried that.. but the answer says 36

Answer 6

oh

Answer 7

lets see if some flaw there in our logic..

Answer 8

and a question.. for the second case where first digit is from {5,7,9}, should the set for second digit be ({5, 7, 9} -1) or {1,3,5,7,9}-1 ? isnt any number with 5,7,9 in first digit larger than 350 so second digit can be any ?

Answer 9

awesome ! you're right !!

but still we get answer as 36+9 = 45 which is incorrect.. .

Answer 10

yeah i tried that.. not sure.

Answer 11

its okay if you cant get it i'll ask teacher tomorrow

Answer 12

45 looks correct to me

Answer 13

ok :D

Answer 14

and for these problems, do you do break the problem into separates cases or ?

Answer 15

yeah here we must break it into 2 cases. it cant get more simpler than this i think...

Answer 16

choose the leftmost digit, now there are 12 possibilities for that digit.
5,7,9 each give 12 numbers > 350
3 gives (12-3) numbers > 350 --- we lose the three for 31-
1 gives 0 numbers > 350
I get 45.
I think you are right @ganeshie8

Answer 17

yes. thanks @telliott99
just enumerated all the permutations. 45 is correct !
PFA

Answer 18

thanks!! what does PFA mean btw

Answer 19

Please Find Attached
when you attach something with ur reply you indicate that with PFA :D