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  • Please,please help me 8 - digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do not occupy odd places, is :

8 - digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do not occupy odd places, is :

  • Option 1)

    160

  • Option 2)

    120

  • Option 3)

    60

  • Option 4)

    48

 

Answers (1)

best_answer

As we have learned

Number of arrangement of like and alike objects -

The number of arrangements that can be formed using n objects out of which r, q and p are identical objects then total number of arrangements=\frac{n!}{p!\ q!\ r!}

Ex. ALLAHABAD

A\rightarrow4

L\rightarrow2

\therefore\ \; \frac{9!}{4!\ 2!}

-

 

 Odd nos - 1,1,3

EVEN nos . - 2,2,4,4

Case (1) ; odd places filled by 2,2,4,4 

No. of ways = (\frac{4!}{2!2!})\times \frac{4!}{2!}= 72

Odd palces filled by 2,2,2,4

NO. of ways = (\frac{4!}{3!})\times \frac{4!}{2!}= 48

72+48 = 120 

 

 

 

 

 


Option 1)

160

Option 2)

120

Option 3)

60

Option 4)

48

Posted by

gaurav

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