SATHEE: Permutations And Combinations Question 197

Permutations And Combinations Question 197

Question: An n-digit number is a positive number with exactly $ n $ digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of $ n $ for which this is possible is [IIT 1998]

Options:

A) 6

B) 7

C) 8

D) 9

Show Answer

Answer:

Correct Answer: B

Solution:

Since at any place, any of the digits 2, 5 and 7 can be used, total number of such positive $ n $ -digit numbers are $ 3^{n} $ . Since we have to form 900 distinct numbers, hence $ 3^{n}\ge 900\Rightarrow n=7 $ .

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Permutations And Combinations Question 197

Question: An n-digit number is a positive number with exactly $ n $ digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of $ n $ for which this is possible is [IIT 1998]

Options:

Answer:

Solution:

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