SATHEE: Permutations And Combinations Question 167

Permutations And Combinations Question 167

Question: Total number less than 3 x $ 10^{8} $ and can be formed using the digits 1,2,3 is equal to

Options:

A) $ \frac{1}{2}(3^{9}+4\times 3^{8}) $

B) $ \frac{1}{2}(3^{9}-3) $

C) $ \frac{1}{2}(7\times 3^{8}-3) $

D) $ \frac{1}{2}(3^{9}-3+3^{8}) $

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Formed number can be utmost of nine digits. Total number of such numbers is $ 3+3^{2}+3^{3}+…+3^{8}+2\times 3^{8} $ $ =\frac{3(3^{8}-1)}{3-1}+2\times 3^{8}=\frac{3^{9}-3+4\times 3^{8}}{2}=\frac{7\times 3^{8}-3}{2} $

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Permutations And Combinations Question 167

Question: Total number less than 3 x $ 10^{8} $ and can be formed using the digits 1,2,3 is equal to

Options:

Answer:

Solution:

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