# Math Help - Permutations Help

1. ## Permutations Help

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?

2. 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: . $_7P_4 \:=\:840$ 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: . $_6P_3 = 120$ ways.

Therefore, there are: . $3\cdot120 \:=\:360$ even numbers.

c) How many of these numbers are odd?

The rest of them: . $840 - 360 \:=\:480$ odd numbers.