Question

How many 4-digit positive integers can be made using the digits 0,1,2,3,4,5 and repetitions of digits are not allowed?

Answer 1

4096

Answer 2

6*6*6*6 = 6^4

Answer 3

oh wait

Answer 4

you might have to remove some trivial cases

Answer 5

the answer at the book is 300 but i don't know how to arrive at the answer

Answer 6

ok it is 5*6*6*6

Answer 7

oh repetition not allowed

Answer 8

so 5*5*4*3

Answer 9

so thats 300

Answer 10

why is the second number 5

Answer 11

ok let me explain the logic

Answer 12

the first number in the thousandth's place is
to choose from { 1,2,3,4,5} , for the hundreth place
you can choose 0 , so you again have 5 choices .

Answer 13

so for example , if you choose 1 for thousandth place, then you have
{ 0,2,3,4,5} numbers to choose for hundredth place.

Answer 14

ooohhh that make sense. I thought it was 5,6,4,3 thanks a lot

Answer 15

if you choose 3 for hundreth place, then you have { 0,2,4,5} for tens place

Answer 16

5643?

Answer 17

oh 5*6*4*3

Answer 18

you're right, it is 5,5,4,3

Answer 19

the trick is you have to add zero to the second choice, third, etc

Answer 20

yup

Answer 21

the zero does not apply to the first choice. so its tricky ;)

Answer 22

thanks again

Answer 23

also to be clear they should say that 0430 is not a 4 digit number for example

Answer 24

also interesting you have to do the choices in order, you cant skip around

Answer 25

this is called multiplication principle by the way

Answer 26

jm, any questions?

Answer 27

5*5*4*3 = 300
Cannot use 0 for the thousands digit, therefore, one of the 5 non-zero digits can be chosen. For the hundreds digit, 0 and 4 of the other numbers can be chosen. The tens digit 4 and the units digit 3.