How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?

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NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)
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  1. 32
  2. 36
  3. 40
  4. 45

Answer (Detailed Solution Below)

Option 1 : 32
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Detailed Solution

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Concept:

A permutation is an arrangement of objects in a definite order.

\(\displaystyle ^n P_r=\frac{n !}{(n-r) !}\),

where, 

           nPr = Permutation

        n = total number of objects

        r = number of objects selected

Calculation:

Numbers between 300 and 400 consist of three digits with the digit at hundred’s place equal to 3.

Since repetition is not allowed and there must be only odd numbers, one’s places can be filled using the digits 1,5,7 and 9 in 4P1 ways.  

Now ten’s place can be filled by using any digits except the digit at one's and hundred's place in 8P1 ways. 

Hence, the required number of numbers = 4P× 8P= 4 × 8 = 32.

∴ The total odd numbers between 300 and 400 in which none of the digits is repeated are 32.

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