Question

how many numbers greater than 1000000 can be formed by using the digits 1,2,0,2,4,2,4?​

Answer 1

Given, digits are 1,2,0,2,4,2 and 4.

So, now we have to find the numbers greater than 1000000

In a 7-digit number, 0 can't appear in the ten lac's place. So, ten lac's place can be filled in 6 ways.

Since repetition of digits isn't allowed and 0 can be used at lac's place, so lac place an be filled again in 6 ways.

Similarly, ten thousand's place, thousand's place, hundred's place, ten's and one's place can be filled in 5, 4, 3, 2 and 1 ways respectively.

Now, in the given digits the digit 2 is repeating thrice whereas the digit 4 is repeating twice.

Hence, the required 7-digit numbers formed

=>6 × 6! /3! × 2! = 360

Answer 2

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$\sf{This\:question\:is\:from:}$

$\sf{Permutation\:and\:combination.}$


$\bold{So,}$

7 digits : 0,1,2,2,2,4,4

( In ascending order)


Any number not beginning from zero would be greater than 1000000.


$\bold{So,}$

Answer would be,

$\frac{6! }{1!3!2!} = 60$

$\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1 \times 3 \times 2 \times 1 \times 2 \times 1} = 60$

$\frac{120}{2} = 60$

$60 \times 60 = 360$


$\bold{Therefore,}$

Possible combinations $=\:360$

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