Question

How many 5-digit numbers exist between 65,000 and 69,999 if no digit is to be repeated in each number?

Answer 1

on the first digit you can use 5-9 so you have 4 options
on the other digits you can use any digit between 0-9, 10 options
So without repeating the first digit you are only left with 9 options for the second, 8 options for the third digit and 7 options on the last digit
Answer is 4 x 9 x 8 x 7 = 2016

Answer 2

cool. thanks! :)

Answer 3

oh. it's rather 5 x 8 x 7 x 6. because at the time you choose a digit in the 3rd place, you have already used 2 digits (6 and the second digit).

Answer 4

oh no. you were right for the '4', but im right for 8x7x6.

Answer 5

so what is the answer? haha. im confused

Answer 6

number: a b c d e
a is '6' (no choice)
b is in 5, 7, 8, 9 (4 choices)
c is in {0,1,....,9} \ {a,b} (8 choices)
d is in {0,1,...,9} \ {a,b,c} (7 choices)
e is ..... (6 choices)

-> \(4\times8\times7\times6\).

Answer 7

ok, i gotchya! thanks! :)

Answer 8

nope, since you can't use 6. and you can't use the second digit. -> you used up two digits already.

Answer 9

... you can't use 6, so the choice for the second digit of the number is limited to 5, 7, 8, 9, not 6! -> only 4 choices.

Answer 10

His answer is right. I cannot use 6 on any digit.

Answer 11

:) few!
yea these questions are a mess

Answer 12

yeah. stupid math project. so the answer is...? im confused again.

Answer 13

4 x 8 x 7 x 6.
———
number: a b c d e
a is '6' (no choice)
b is in 5, 7, 8, 9 (4 choices)
c is in {0,1,....,9} \ {a,b} (8 choices)
d is in {0,1,...,9} \ {a,b,c} (7 choices)
e is ..... (6 choices)
———

Answer 14

ok, thank you!

Answer 15

1344 i guess.

Answer 16

good enough.