Aptitude 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,

$n = 360+180$

$= \textbf{540 ways}.$

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