Calculate the number of natural numbers between 100 to 1000 such that atleast 1 of their digits is 7.
Answers
Thw number of natural numbers between 100 and 1000 means that it is three digit.
When only one digit is 7
i) when the one's place is 7 = 8 × 9 × 1 ways = 72 ways
ii} when the ten's place is 7 = 8 × 9 × 1 ways = 72 ways
iii) when hundredth place is 7 = 9 × 9 ways = 81 ways
Therefore, when only one digit is 7 = 72 + 72 + 81 ways = 225 ways
When two digits are 7
i) when ones and ten's place is 7 = 8 ways
ii) when hundredth and ten's place is 7 = 9 ways
iii) when one's and hundredth is 7 = 9 ways
Therefore, when two digits are 7 = 26 ways
When all three digits are 7
only 1 way is possible = 1 way
Therefore, the total number of ways = 225 +26 +1
= 252 ways
Thw number of natural numbers between 100 and 1000 means that it is three digit.
When only one digit is 7
i) when the one's place is 7 = 8 × 9 × 1 ways = 72 ways
ii} when the ten's place is 7 = 8 × 9 × 1 ways = 72 ways
iii) when hundredth place is 7 = 9 × 9 ways = 81 ways
Therefore, when only one digit is 7 = 72 + 72 + 81 ways = 225 ways
When two digits are 7
i) when ones and ten's place is 7 = 8 ways
ii) when hundredth and ten's place is 7 = 9 ways
iii) when one's and hundredth is 7 = 9 ways
Therefore, when two digits are 7 = 26 ways
When all three digits are 7
only 1 way is possible = 1 way
Therefore, the total number of ways = 225 +26 +1
= 252 ways