Solution:
(a) Case I 1-digit number
In 1-digits number 7 corner in 1 ways
Case II 2-digit number
In 2-digit number 7 corner in 19 ways.
[∴ 17, 27, 37, 47, 57, 67, 70, 71,72, 73, 74, 75, 76, 77,78, 79, 87, 97]
Case III 3-digit number
(i) When 7 corners in unit place, the rest of the two places we choose any number other than 7
i.e.,8x 9 = 72 way
(ii) When 7 corners is ten place, the rest of the two places we choose any number other than 7,
i.e.,8 x 9 = 72 way
(iii) When 7 corners in hundred place, then we choose in
9 x 9 = 81 ways
(iv) When 7, 7 corners in any two places and rest of the one place we choose any number other than 7.
Then, the number of ways = 26 ways
(v) When all three places have 7 is only 1 ways.
∴Total number of times 7 corners from 1 to 1000
= 1 +19 + 72 + 72 + 81 + 26 + 1= 272
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