Question
How many 7 digit even numbers can be formed using all of the digits 0,1,1,2,3,4?
The answer is 1320. I tried 7!/2! but I know its supposed to be even, so it's not right to do 2!. How do I get to 1320?
The answer is 1320. I tried 7!/2! but I know its supposed to be even, so it's not right to do 2!. How do I get to 1320?
Answers
Luise
Sorry, the digits are 0,1,1,2,3,4,5
Reiny
let's first of all assume that the two 1's are distinguishable, e.g. one is red, the other blue
case1, our even number ends in a zero
number of such cases = 6x5x4x3x2x1x= 6! = 720
but the two 1's ARE distinguishable, so
the number of evens that end in a zero are 720/2 = 360
case2, our even number ends in either 2 or 4
and we of course can't start with a zero.
fill the end first
number of ways for our number
= 2 x 5 x 5 x 4 x 3 x 2 x 1 = 1200
taking care of the same 1's
number of case2 numbers = 1200/2 = 600
total number = 600 + 360 = 960
I disagree with the answer of 1320
case1, our even number ends in a zero
number of such cases = 6x5x4x3x2x1x= 6! = 720
but the two 1's ARE distinguishable, so
the number of evens that end in a zero are 720/2 = 360
case2, our even number ends in either 2 or 4
and we of course can't start with a zero.
fill the end first
number of ways for our number
= 2 x 5 x 5 x 4 x 3 x 2 x 1 = 1200
taking care of the same 1's
number of case2 numbers = 1200/2 = 600
total number = 600 + 360 = 960
I disagree with the answer of 1320