Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. How many positive integers $n$ can be form using the digits $3,4,4,5,6,6,7$; if we want $n$ to exceed $60,00,000$?
 ✖ A. $320$ ✖ B. $360$ ✔ C. $540$ ✖ D. $720$

Solution:
Option(C) is correct

As per the given condition, number in the highest position should be either 6 or 7, which can be done in 2 ways.

If the first digit is 6, the other digits can be arranged in $\dfrac{6!}{2!} = 360$ ways.

If the first digit is 7, the other digits can be arranged in $\dfrac{6!}{2!×2!} = 180$ ways.

Thus required possibilities for,

$n = 360+180$

$= \textbf{540 ways}.$

(2) Comment(s)

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I like your exercises but they are very obvious and simple.

It is possible to ask you guys a question?

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