how many numbers greater than 500000 can be made from digits 2,3,4,5,6,and 7 without repeatition if the number is odd?
+128474 2, 3, 4, 5 , 6 , 7
If 6 is chosen first , we have 3 possibilities for the last digit (3, 5 or 7)
And we have 4! = 24 ways to permute the remaining digits
So 1 * 4! * 3 = 1* 24 * 3 = 72
If either 5 or 7 is chosen first, we have 2 ways to choose the last digit and 4! ways to permute the remaining digits = 2 * 4! * 2 = 4 * 24 = 96
[For example....if we choose 5 first, we have two choices for the last digit, either 3 or 7.....and 4! ways = 24 ways to permute the middle four digits '
So....the total possibiities = 72 + 96 = 168
