There are six spots to consider, how many combinations for each?
All numbers need to appear at least once and for the last two spots they can be the same or different. The answer will be of the form.
Do you follow?
Hello, prasum!
Find the number of 6-digit numbers that can be made with digits {1, 2, 3, 4}
if all digits are to appear in the number at least once.
Let the four digits be:
Select one of each digit: .
There are two cases to consider.
[1] The other two digits are the same: . choices.
. . .The number is of the form:
. . .The digits can be permuted in: ways.
. . .Hence, there are: . such numbers.
[2] The other two digits are different: . choices.
. . .The number is of the form:
. . .The digits can be permuted in ways.
. . .Hence, there are: . such numbers.
The answer is: . numbers.