Question:

How many four digit numbers abcdabcd exist such that aa is odd, bb is divisible by 33, cc is even and dd is prime?

Updated On: Jun 7, 2024
  • 380
  • 360
  • 400
  • 520
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The Correct Option is C

Solution and Explanation

We know that, the odd numbers are
{1,3,5,7,9} \{1,3,5,7,9\}
n(a)=5\therefore n(a)=5
Divisible by 33 are {0,3,6,9},n(b)=4\{0,3,6,9\}, n(b)=4
Even numbers are {0,2,4,6,8},n(c)=5\{0,2,4,6,8\}, n(c)=5
and prime numbers are {2,3,5,7},n(d)=4\{2,3,5,7\}, n(d)=4
\therefore Four-digit numbers abcdabcd exist
=5454=5 \cdot 4 \cdot 5 \cdot 4
=400=400
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Questions Asked in KEAM exam

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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.