The number of all natural numbers up to 1000 with non-repeating digits is:
Explanation:
Single-digit such numbers = 9
2-digit such numbers: __ __ Ten’s digit can be filled in 9 ways (i.e., 1, 2, 3, …, 9) Unit’s digit can be filled in 9 ways (i.e., any of the 10 single digits except the one at ten’s place) ⇒ Total such 2-digit numbers = 9 × 9 = 81
3-digit such numbers: __ __ __ Hundred’s digit can be filled in 9 ways (i.e., 1, 2, 3, …, 9) Ten’s digit can be filled in 9 ways (i.e., any of the 10 single digits except the one at hundred’s place) Unit’s digit can be filled in 8 ways (i.e., any of the 10 single digits except the ones at hundred’s and ten’s place) ⇒ Total such 3-digit numbers = 9 × 9 × 8 = 648
∴ Total such numbers = 9 + 81 + 648 = 738.
Hence, option (c).
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