How many three-digit numbers are there?

1.	How many three-digit numbers are there?
Answer» Let us assume that we have three boxes. First box can be filled with any one of the nine digits (zero not allowed at first position) Therefore, possibilities are ⁹C₁ The second box can be filled with any one of the ten digits Therefore the available possibilities are ¹⁰C₁ Third box can be filled with any one of the ten digits Therefore the available possibilities are ¹⁰C₁ Thus, the total number of possible outcomes are ⁹C₁ × ¹⁰C₁ × ¹⁰C₁ = 9 × 10 × 10 = 900.

Answer»

Let us assume that we have three boxes.

First box can be filled with any one of the nine digits (zero not allowed at first position)

Therefore, possibilities are ⁹C₁

The second box can be filled with any one of the ten digits

Therefore the available possibilities are ¹⁰C₁

Third box can be filled with any one of the ten digits

Therefore the available possibilities are ¹⁰C₁

Thus, the total number of possible outcomes are ⁹C₁ × ¹⁰C₁ × ¹⁰C₁ = 9 × 10 × 10 = 900.

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