Question

Find the number of odd integers between 1000 and 8000 in which no digit is repeated

Answer 1

There are two restrictions in operating this question:

1. For a number to be odd the unit digit should be either 1 ,3 , 5 , 7 , 9

2. Thousands place cannot be filled with 8 or 9

For units digit when it is filled with 9 the thousands place can be filled in 7 ways namely any digit from 1 to 7 and the remaining two places can be filled in 8 ×7 =56 ways

so, the total number formed in this way 56×7= 392

Now if units place is filled with any of the four digits 1,3,5 or 7 , the thousands place can be filled in 6 ways( zero will be excluded) and the remaining two places can be filled in 8 × 7 = 56

So, the total number formed in this way 56×6×4= 1344

Hence, total numbers are 392+1344 =1736

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Hope this will help you...