SOLUTION: How many four-digit odd integers greater than 6000 can be formed from the digits 0,1,3,5,6 and 8, if no digit can be used more than once?

Question 341008: How many four-digit odd integers greater than 6000 can be formed from the digits 0,1,3,5,6 and 8, if no digit can be used more than once?
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
Digits are 0,1,3,5,6,8
we have to fill four places ABCD, D is unit digit, B is tenth digit and so on..
number must be greater than 6000 so,
no. of ways to fill position of A is 2 (6 or 8)
case 1: when 6 is at A (first digit)

no. of ways to fill the position D = 3 (1,3 or 5)
no. of ways to fill the position B = 4 (only 4 digit remaining)
no. of ways to fill the position c= 2 (only 3 digit )

total no. of ways to form odd integer starting from 6 = 3*4*2= 24
case 2: when 8 is at A (first digit)

similarly, no. of ways to fill the position D = 3
no. of ways to fill the position B = 4
no. of ways to fill the position C = 3
total no. of ways to form odd integer starting from 8 = 3*4*2 =24

total no. of four digit odd integers greater than 6000 = 24+24 = 48
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