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.

Asked by Pawan chhipa | 8th Nov, 2012, 10:47: AM

Expert Answer:

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

Answered by  | 8th Nov, 2012, 10:56: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.