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  2. I have a doubt, kindly clarify. - Permutations and combinations - JEE Main
# Engineering

All possible numbers are formed using the digits 1,1,2,2,2,2,3,4,4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :

  • Option 1)

    180

  • Option 2)

    160

  • Option 3)

    175

  • Option 4)

    162

 

Answers (1)
S solutionqc

1,1,2,2,2,2,3,4,4=9 \; digit

We have total 4 even place and 3 odd digit = 1,1,3

Number of way placing odd digit at even places =^{4}C_{3}\frac{3!}{2!}=4\times3=12

Number of ways placing even digits =\frac{6!}{4!2!}=\frac{6\times5}{2}=15

So total number of ways =12\times15=180


Option 1)

180

Option 2)

160

Option 3)

175

Option 4)

162

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