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?
2 answers
Sorry, the digits are 0,1,1,2,3,4,5
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