how many four digit numbers can you form with the digits 1, 2, 3, 4, 5, 6, 7 if no digit is repeated
b) How many of these digits are even?
c) how many of these digits are odd?
Hello, MHurricane!
How many f4-digit numbers can you form with the digits 1, 2, 3, 4, 5, 6, 7
a) if no digit is repeated?
There are: .$\displaystyle _7P_4 \:=\:840$ possible 4-digit numbers.
b) How many of these numbers are even?
The last (rightmost) digit has 3 choices: {2, 4, 6}
Choose 3 of the other 6 digits.
. . They can be arranged in: .$\displaystyle _6P_3 = 120$ ways.
Therefore, there are: .$\displaystyle 3\cdot120 \:=\:360$ even numbers.
c) How many of these numbers are odd?
The rest of them: .$\displaystyle 840 - 360 \:=\:480$ odd numbers.