First slide

Permutations

Question

The number of natural numbers with distinct digits is

Moderate

A

$9^{10} - 1$
B

$10^{10} - 9^{10}$
C

$9^{10} x 1$
D

none of these

Solution

Required number of natural numbers
$=^{9} P_{1} + 9 \times^{9} P_{1} + 9 \times^{9} P_{2} + \dots + 9 \times^{9} P_{9}$

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