Question

A number of four different digits are formed by using the digits 1, 2, 3, 4, 5, 6, 7 in all possible ways without repetition.

How many of them are greater than 3400?

Answer 1

5*4*5*4=400

Answer 2

So, here you are given with 4 digit number..

So, every digit you can fill up with 1,2,3,4,5,6,7..

But you want number greater than 3400, so:

First place will be either : 3, 4,5,6,7 ( In 4 ways you can fill first place)

Answer 3

*5

Answer 4

yes i done that above

Answer 5

You have done the case when first digit is starting with 3, right?

Answer 6

Getting my point?

Answer 7

second in 4,5,6,7 so 4 ways
third in 1,2,3,4,5,6,7, so 7 ways but repition is not allowed

Answer 8

so 5 ways
fourth in 7 ways cuz of reptition 4 ways

Answer 9

You are not getting me..

Answer 10

Tell me one thing 4001 > 3400 or not??

Answer 11

yes

Answer 12

First place you can fill up with 3,4,5,6, and 7 no doubt about it five ways..

But you need to be careful at second place filling..

If you have chosen you first digit as 3, then you will get one case..

If you will chose your first digit as 4,5,6 and 7, then that will form another case..

Look here:

Suppose you chose 3 as your first place, so second place only 4,5,6,7 can come..

But if you chose first digit as any one of 4,5,6,7 then your second digit can be 1,2,3,5,6 and 7 ( I chose 4 as first digit, so 4 will not include here). So this will be another case..

Answer 13

I simply mean if you chose 4,5,6,7 as your first digit, then you will get:

4*6*5*4 = 480.

Getting me??

Answer 14

first digit in 5ways u wrote 4

Answer 15

I suggest you to break your question into small parts if you are getting confused..

Say I am breaking like this for you: As you need number greater than 3400:

So 1> Fix 3 as your first digit and try to find all number greater than 3400.
2. Make any number starting with 4,5,6,7 (as this will automatically be greater than 3400)..

Answer 16

First digit in 4 ways, for one case.

First digit in only 1 way for another case..

Answer 17

So, Fist case I am doing for you:

I said, to fix 3 as your first digit and find numbers greater than 3400, you can surely say that number formed will be greater than 3400 but less than 4000 as I am fixing my first digit as 3.. Getting this one?

Answer 18

*First case

Answer 19

Are you busy right now or doing something else? I want your attention here..

The question you have posted is really a good one... :) Try to understand it, you are just there.. :)

Answer 20

yes there.:)

Answer 21

Getting the first case?

Answer 22

but if 3401,3402 has we have 5 ways

Answer 23

But I am considering it in one case no??

Answer 24

Hey wait..

I have categorized numbers between two cases..

1. Numbers from 3400 to 3999 (this will consider your 3401, 3402)

2. Number above 4000

Answer 25

Say if you fix 3 as your first digit, then you will all four digit number starting from 3?? Am I right here?

Answer 26

yes

Answer 27

Now if you have fix your first digit as 3, in how many ways you can fill first place?? Be careful while answering..

Answer 28

5 ways

Answer 29

First place with 5 ways??

You have set your first place with digit 3, then how can you change it with 4,5,6,or 7??

Answer 30

then second will be greater than or equal to 4 ->4,5,6,7 in 4 ways

Answer 31

Firstly tell me of first place..

Don't be fast... :)

Answer 32

Wait, just take breathe fully for two minutes.. :)

Answer 33

1 ways sorry

Answer 34

Yes, see, taking breathe deeply helps your brain to work properly as it supplies proper supply of oxygen which now you are not getting.. :P

Answer 35

then 1*4*5*4

Answer 36

first place is 3 means 1 way

Answer 37

Yes first in 1 way.
Second in 4 ways, (4,5,6,7)

Look for third place more carefully..

Answer 38

5 ways

Answer 39

Okay, third in 5 ways (Good)

And 4th place in 4 ways, so you got total : 80

Answer 40

yes

Answer 41

Now this is one case where you have taken 3 as your rigid first place..

Now move to another case waiting for use to be analyzed.

Now tell me, if I use 4,5,6 and 7 as first digit, then all numbers will automatically be greater than 3400, right??

Answer 42

in second case 1st digit is 4 ways ,2nd in 6 and ,3rd in 5 ,th in 4 ways

Answer 43

Now, here you can fill your first place as 4,5,6 and 7.. (don't consider 3 here as you have considered it in first case already)

Now tell me how many ways you will get?

Answer 44

in second case 1st digit is 4 ways ,2nd in 6 and ,3rd in 5 ,th in 4 ways

Answer 45

480+80=560

Answer 46

is it right?

Answer 47

@waterineyes

Answer 48

It must be right..

Sorry, Openstudy was not opening for me earlier.. :(

Answer 49

i think i am sure

Answer 50

I am sure too.. :) Yes you are right.

Answer 51

thank you so much:)

Answer 52

You are welcome dear..:)