How many different 4-digit numbers are there such that the number is even, none of the digit repeat and first digit is not zero
# of ways
=total - 4-digit odd numbers
=( 9 ) ( 9 ) ( 8 ) ( 7 ) - ( 8 ) ( 8 ) ( 7 ) ( 5 )
=2296
explanation...10 numbers to choose: 0-9
total:
1st digit--> 9 choices (eliminate 0)
2nd digit--> 9 choices (u've already chosen one number for the 4th digit)
3rd digit--> 8 choices (chosen 2 already, 8 left)
4th digit--> 7 choices (chosen 3 already, 7 left)
odd:
4th digit-->5 choices (1,3,5,7,9)
1st digit-->8 choices (9 numbers remained, yet u cannot use 0 for this )
2nd digit-->8 choices (chosen two already)
3rd digit-->7 choices left
wish me good luck,
im having a test on binomial theorem tomorrow...
