Question

find the numbers greater than 23000 that can be formed from the digits 1,2,3,4,5,6 a digit used only once ?
a ) 60
b) 96
c) 90
d)none

Answer 1

@ganeshie8 @dan815 @ParthKohli @bahrom7893
please help
me

Answer 2

@uri @inkyvoyd

Answer 3

@Nurali

Answer 4

@Gabylovesyou

Answer 5

@jhonyy9

Answer 6

@ikram002p teacher help me ? ??

Answer 7

first bigest number
23145
hehe i think its permentation stuff xD

Answer 8

and all numbers can be formed from all of them(6 digits number ) is >23000

Answer 9

How can i get answer
actually it is my university entry test practice question and i stop in this question when i was practicing ...

Answer 10

so the problem with the 5 digits number u would have 2 conditions :-
1_ it cant have the fifth digit as 1
2_ if the fifth digit is 2 then 4th digits cant be 1

Answer 11

so it would be
6! + something lol
which make no sense according to ur options
@ganeshie8 what do u think ?

Answer 12

option D

Answer 13

ohh , hehe chosing non of them make me confused :P

Answer 14

total possible numbers = 6!

Numbers less than 23000 :
numbers starting with `1` = 5!
numbers starting with `21` = 4!
numbers starting with `23` = 1

so the required answer would be : 6! - (5! + 4! + 1)

Answer 15

oh ! mmm
how is that -.-

Answer 16

i mean 6! for 6 digits numbers
hmm

Answer 17

_ _ _ _ _

5 spaces to be filled with 6 digits

Answer 18

first space can be filled in : 6 ways
second space can be filled in : 5 ways
...
fifth space can be filled in : 2 ways

so total possible numbers = 6x5x...x2 = 6!

Answer 19

see my method and i get the answer it is matched with the option
i) 1st place is filled by 1(2) and 2nd is also 1(3)
where as 3 place is filled by 4 ways(1,4,5,6)
and 4the place is filled by 3 ways
and 5th place is filled by 2 ways
total : 1 x 1 x 4 x 3 x 2 = 24

ii) 1st place is filled by 4 ways ( 3,4,5,6)
2nd place is filled by 5 ways
3rd by 4 ways
4th place by 3 ways
and 5th place is 2 ways
total : 4 x 5 x 4 x 3 x 2 =480
grand total is 480 + 24 = 504
am i correct ???

Answer 20

ganesh , a number could be formed from 6 digits ( at most ) begger than 23000
means
1_ all 6 digits number
2_ 5 digits number exept :-
1_ it cant have the fifth digit as 1 , 1 XXXX
2_ if the fifth digit is 2 then 4th digits cant be 1 21XXX

Answer 21

so i guess its

6! +6! - (5! + 4! + 1)

Answer 22

yes i am correct because the last one i have solved and i got the correct answer and the smae method i applied here but i could not get the answer so Answer D is correct

Answer 23

omg! yes yes you're right, i have counted only 5 digit numbers, mistake >.<

Answer 24

how ever lol
both get non of options xD
it might be my way to interept the question

Answer 25

@ganeshie8 is my method correct for solving this

Answer 26

whats ur method O.O

Answer 27

see in the above

Answer 28

i think we both did the same mistake...
we need to count both 5 and 6 digit numbers as ikram pointed out earlier

Answer 29

I need to study factorials more I think, but I eventually got the same answer as you @Haseeb96 good job! I guess I didn't really know that it was ok to add factorials, but I guess if you think about it it kind of makes sense.

Answer 30

mm kai :O

Answer 31

Is 504 wrong? There's a lot of discussion here so I just sort of skimmed most of it.

Answer 32

there will be atleast 6! = 720 `6 digit numbers`
so the answer better be some number greater than 720

Answer 33

How? There are only 5 places and 6 digits so there would be 6!/1! ways of arranging it at the maximum not at the minimum. But we have a restriction on the first two digits and they are:

We can't have 1 for the first digit

If the first digit is 2, then the second digit can't be 1.

So in the case that the first digit is 2 we have 4 possibilities for the second digit (3,4,5,6) and then the next 3 digits can be any of the leftover digits so we have used up 2 and have 4 total so that means there are 4!/1! ways to pick the last 4 digits. So for this case we have 1*4*4! This means 1 possibility for the first digit being 1, 4 for the second digit being not 1 or 2, and the last 3 digits are arranged 4!/1!.

The other case is simply that the first digit is any number greater than 2, so we have (3,4,5,6) meaning 4 possibilities. The next numbers have no restrictions so there is simply 5!/1! ways of arranging the last 4 digits. Meaning we have 4*5!.

Adding these two independent ways or organizing them together to get the total number of ways to rearrange them we have:

4*4!+4*5!

factor out a 4!

(4+4*5)*4!

24^2=576

So it looks like I might have messed up last time or this time because I'm getting a higher number by a factor of 4.

Answer 34

we're not given that they want only 5 digit numbers, right ?

Answer 35

576 = # of 5 digit numbers
6! = # of 6 digit numbers

so total would be 6! + 576

Answer 36

im still not sure how the OP got 504 earlier... leme check again :)

Answer 37

yeah earlier he missed multiplying 24 by 4 :
```
see my method and i get the answer it is matched with the option
i) 1st place is filled by 1(2) and 2nd is also 1(3) ********MISTAKE*******
where as 3 place is filled by 4 ways(1,4,5,6)
and 4the place is filled by 3 ways
and 5th place is filled by 2 ways
total : 1 x 1 x 4 x 3 x 2 = 24 ********MISTAKE*******

ii) 1st place is filled by 4 ways ( 3,4,5,6)
2nd place is filled by 5 ways
3rd by 4 ways
4th place by 3 ways
and 5th place is 2 ways
total : 4 x 5 x 4 x 3 x 2 =480
grand total is 480 + 24 = 504
am i correct ???
```

Answer 38

Oh I see, I was looking for 5 digit numbers only. haha. I guess in any case, it's multiple choice.