Question
Thu November 08, 2012 By: Pawan Chhipa
 

How many numbers are there between 100 and 1000 which have exactly one of their digit as 7. sir,please made him understood this ques is in easy way.

Expert Reply
Thu November 08, 2012
The numbers between 100 and 1000 having 7 as exactly one of their digits can be classified into three types:
 
1) When the units place has 7:
Tens place can have any one of the digits except 7. So, it can be filled in 9 different ways. The hundreds place can have any one of the digits except 0 and 7. So, it can be filled in 8 different ways.Therefore, there are 9 x 8 = 72 such numbers.
 
2) When the tens place has 7:
The units place can have any one of the digits except 7. So, it can be filled in 9 different ways. The hundreds place can have any one of the digits except 0 and 7. So, it can be filled in 8 different ways.Therefore, there are 9 x 8 = 72 such numbers.
 
3)
When the hundreds place has 7:
Units place can have any one of the digits except 7. So, it can be filled in 9 different ways. The tens place can have any one of the digits except 7. So, it can be filled in 9 different ways.Therefore, there are 9 x 9 = 81 such numbers.
 
Hence the required number of numbers = 72 + 72 + 81 = 225
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