Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. How many natural numbers less than a lakh can be formed with the digits 0, 6 and 9?
 ✔ A. 242 ✖ B. 243 ✖ C. 728 ✖ D. 729

Solution:
Option(A) is correct

The digits to be used are 0,c6 and 9.

The required numbers are from 1 to 99999.

The numbers are five digit numbers.

Therefore, every place can be filled by 0, 6 and 9 in 3 ways.

Total number of ways $= 3×3×3×3×3 = 3^5$

But 00000 is also a number formed and has to be excluded.

Total number of numbers $= 3^5 -1$

$= 243-1$

$= \textbf{242}$