Question:

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 :

Updated On: June 02, 2025
  • 175
  • 162
  • 160
  • 180
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The Correct Option is D

Solution and Explanation

The correct answer is D:180
Given that: The periodic number to be formed using digits \(1,1,2,2,2,2,2,3,4,4\) to be taken all at a time.
[Note: Means;it is a clear case of combination as only selection is important here]
\(\therefore 4_{C_{3}}\times\frac{3!}{2!}\times\frac{6!}{2!\times4!}=180\)  \((\therefore n_{c_{k}}=\frac{n!}{(n-k)!,k!})\)\((4_{c_{3}}=\frac{4!}{1!\times3!})\)
Combination
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JEE Main Notification

Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.