Question

The digits 0, 1, 2, 3, and 4 are to be used to form a five-digit number. How many different numbers can be formed if
a) repetitions are permitted?
b) repetition is not allowed?
c) the number must be odd and repetitions are not allowed?
d) the number must be greater than 30,000 and repetition is not allowed?

Answer 1

Can you please help me @iGreen Thank you :)

Answer 2

okay repetitions are allowed
_ _ _ _ _
for the first digit we can pick 1 to 4
the 2nd to last digit we can pick 0 to 4
so

4*5*5*5*5 = total 5 digit numbers with repetition allowed

Answer 3

repetitions not allowed
_ _ _ _ _
we still have 4 numbers to pick from
1 to 4 in the first part
now we have 3 of those numbers left and the 0 number
so we have 4 choices to pick from in the 2nd one
and then 3 and the 2 and 1

4*4*3*2*1= total number of 5 digit numbers with no repetition is allowed

Answer 4

number must be odd so

the last digit has to end with 1 or 3
only 2 choices for the last digit, then we have 4 choices left for the 2nd last
then 3, then 2 then 1
_ _ _ _ _
1*2*3*4*2 = total number of odd digits with no repetition

Answer 5

for a number to be greater than 30000
this means the first digit is 3 or 4 so 2 choices
and no repeitions are allowed so

_ _ _ _ _
2*4*3*2*1= total number of digits greater than 30000, with no repetition allowed

Answer 6

Do you understand >_>

Answer 7

you've been awfully quiet

Answer 8

@dan815 thank you so much :D sorry my internet connection is very slow i had to refresh it mulitple times :))

Answer 9

in a). why is that only 1-4 can be used in the first digit?

Answer 10

If you had 0 for the first digit it wouldn't be a 5-digit number, it'd be a 4-digit number!