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Tamil Nadu Board of Secondary EducationHSC Science Class 11

How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5 ? if the repetition of digits is not allowed - Mathematics

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Question

How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed

Sum
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Solution

The given digits are 0, 1, 2, 3, 4, 5

To find the possible 3-digit odd numbers.

Repetition of digits is not allowed:

Hundred's Ten's Unit

Since we need 3-digit odd numbers the unit place can be filled in 3 ways using the digits 1, 3 or 5.

Hundred’s place can be filled in 4 ways using the digits 0, 1, 2, 3, 4, 5 excluding 0 and the number placed in unit place.

Ten’s place can be filled in 4 ways using the digits 0, 1, 2, 3, 4, 5 excluding the digit placed in the hundred’s place.

Therefore, by the fundamental principle of multiplication

The number of 3 – digit odd numbers formed without repetition of digits using the digits 0, 1, 2, 3, 4, 5 is

= 4 × 4 × 3

= 48

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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.1 [Page 166]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.1 | Q 7. (i) | Page 166

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