How many numbers greater than 600 can be formed from the digits 2,3,4,6 if
The first digit can only be 6
a. No digit is used twice
Three-digit numbers:
Choose the 1st digit 1 way, as 6.
Choose the 2nd digit as any of the 3 remaining digits {2,3,4}.
Choose the 3rd digit as any of the 2 remaining digits.
That's 1*3*2 = 6 three digit numbers. We can just list them:
1. 623
2. 624
3. 632
4. 634
5. 642
6. 643
Four-digit numbers:
That's also 6 because in each of the cases above we just put
the 1 remaining digit on the end of each of those 6 three-digit
numbers above.
1. 6234
2. 6243
3. 6324
4. 6342
5. 6423
6. 6432
Total: 6+6 = 12.
b. No such rule exists
Infinitely many because 666666666666666666666666666666
is possible or even numbers that stretch out to the moon. :)
Edwin