Question

How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if:
a) there are no repeats allowed?
b) the number is odd and no repeats allowed?
c) the number is greater than 4000 and no repeats are allowed?
d) the number is greater than 4000 and repeats are allowed?

Answer 1

No repeats allowed means that there are 7 choices for the first slot, 6 slots for the second, 5 for the third, 4 for the last. Thus, it's 7*6*5*4.
If the number is odd, then we have 3 slots for the last slot (the number should end in 3, 7, or 9), 6 for the first, then 5, then 4. This translates to 3*6*5*4.
Can you do the rest? :)

Answer 2

Trying, but still a little confused.

Answer 3

A hint for c and d: First consider what choices you have to the first digit.

Answer 4

Okay so for c) I noticed that I could only pick 6, 7 or 9 for the first digit, since the number is over 4,000. This leaves me with 3 choices. So I guess the answer would be 3*6*5*4?

Not sure about d).

Answer 5

Not quite. You could also pick 4 and since repeats are not allowed, the smallest number you could form that satisfies all this is 4023>4000. Thus, it's 4*6*5*4.
For d, it's almost the same and since repeats are allowed, the answer is 4*7*7*7-1 because we exclude the number 4000 from the count.
Feel free to ask for any clarifications.

Answer 6

I have just one. Why there a '-1'?

Answer 7

If we count the way I just did, 4000 can be formed, and 4000 is not greater than 4000, so I had to exclude that one.

Answer 8

Oh okay! Well, thank you very much! :D

Answer 9

No prob. :)