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?

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- February 8th 2009, 06:02 AMazuki[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? - February 8th 2009, 06:10 AMPlato
- February 8th 2009, 09:08 AMSoroban
Hello, azuki!

Quote:

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?

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: . numbers with no 4's.

(2) One 4

There are 3 possible positions for the 4.

. . The other two digits have: choices.

There are: . numbers with one 4.

(3) Two 4's

There are 3 possible positions for the two 4's.

. . There are choices for the fourth digit.

There are: . numbers with two 4's.

(4) Three 4's.

There is only number with three 4's: .

Answer: . numbers.