# Math Help - [SOLVED] Permutation and Combination Question 1

1. ## [SOLVED] Permutation and Combination Question 1

How manu four-digit numbers greater than 5000 can be formed from the digits 0,1,2,3,4,5 if
a) all digits may be repeated (I get 215, I just want to confirm if I am right)
b) only the digit 4 may be repeated?

2. Originally Posted by azuki
how manu four-digit numbers greater than 5000 can be formed from the digits 0,1,2,3,4,5 if
a) all digits may be repeated (i get 215,) correct
b) only the digit 4 may be repeated?
correct

3. Hello, azuki!

How many four-digit numbers greater than 5000
can be formed from the digits 0,1,2,3,4,5 if

b) only the digit 4 may be repeated?
The first digit must be 5: . $5\:\_\:\_\:\_$

There are 4 cases to consider . . .

(1) No 4's
Then we have a choice of {0, 1, 2, 3}.
. . The second digit has 4 choices.
. . The third digit has 3 choices.
. . The fourth digit has 2 choices.
There are: . $4\cdot3\cdot2 \:=\:{\color{blue}24}$ numbers with no 4's.

(2) One 4
There are 3 possible positions for the 4.
. . The other two digits have: $4\cdot3 \:=\:12$ choices.
There are: . $3\cdot12 \:=\:{\color{blue}36}$ numbers with one 4.

(3) Two 4's
There are 3 possible positions for the two 4's.
. . There are $4$ choices for the fourth digit.
There are: . $3\cdot4\:=\:{\color{blue}12}$ numbers with two 4's.

(4) Three 4's.
There is only ${\color{blue}1}$ number with three 4's: . $5444$

Answer: . $24+ 36 + 12 + 1 \:=\:73$ numbers.