First slide

Permutations

Question

The number of natural numbers less than one million that can be formed by using the digits, $0, 2$ , and 3 is

Moderate

A

728
B

726
C

730
D

732

Solution

The number of k digit natural numbers formed by using the digit and 3 is $2 (3^{k - 1})$
$∴$ Number of natural numbers less than one million formed by $0, 2$ and 3 is
$\begin{array}{l} = 2 + (2) (3) + (2) (3^{2}) + 2 (3^{3}) + 2 (3^{4}) + 2 (3^{5}) \\ = 728 \end{array}$

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