How many six digit number contains exactly 4 different digit?
Any help would be greatly appreciated?
Thanks,
Hello, a69356!
I will assume that the number may begin with zero.How many six-digit numbers contains exactly 4 different digits?
First, select 4 digits from the available 10 digits.
. . There are: . choices.
Then there are two possible distributions of the digits.
. . .
Case (1): .
. . We have a Triple and three Singletons.
There are 4 choices for the Triple
Then the letters can be arranged in: ways.
There are: .
Case (2): .
. . We have two Pairs and two Singletons.
There are: choices for the two Pairs.
Then the letters can be arranged in: ways.
There are: .
Therefore, there are: . six-digit numbers
. . that contain four different digits.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
If leading zeros are not allowed, consider this fact:
. . One-tenth of the above numbers begin with zero.