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  • Total number of 6-digit numbers in which only the digits 1,3,5,7 and 9 appear and each of these digit appears at least once, is : Option: 1   &

Total number of 6-digit numbers in which only the digits 1,3,5,7 and 9 appear and each of these digit appears at least once, is :
Option: 1 5^{6}      

Option: 2 \frac{1}{2}(6!)

Option: 3 6!

Option: 4 \frac{5}{2}(6!)
 

Answers (1)

best_answer

PERMUTATION OF OBJECTS WHEN FEW ARE IDENTICAL -

If there n objects of which p objects are of one type, q objects of another type, r objects of yet another type and all others are distinct, the total number of ways of arranging all the objects is \\\mathrm{\frac{n!}{p!q!r!}}

 

Now,

6 places, 5 digit so one digit will repeat

First select the digit to be repeated: 5 options for this

Then arrange these 6 digits in 6 places : 6! / 2!

So, total: 5\times \frac{6!}{2!}

Correct Option (4)

Posted by

Ritika Jonwal

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