First slide

Permutations

Question

How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is allowed) ?

Moderate

A

1024
B

810
C

2346
D

None of these

Solution

Case I : When number in two digits.
Total number of ways $=^{9} C_{1} \times^{9} C_{1} = 9 \times 9 = 81$
Case II : When number in three digits
Total number of ways $=^{9} C_{1} \times^{9} C_{1} \times^{9} C_{1} = 9 \times 9 \times 9 = 729$
$∴$ Total number of ways = 81+ 729 =810

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