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

How many three-digit odd numbers can be formed by using the digits 0,1,2,3,4,5? if (i) the repetition of digit

Exercise 4.1 · Q7

0,1,2,3,4,5

(i) the repetition of digits is not allowed

(ii) the repetition of digits is allowed.

Tamil Nadu DgeTextbookSubjectiveImportance★★★★★

5% · 7/134 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Digits available: $0,1,2,3,4,5$ ; the units digit must be one of $1,3,5$ for the number to be odd.

Step 1. (i) Without repetition. Units: $3$ choices ( $1,3,$ or $5$ ). For each such choice, hundreds excludes $0$ and the used units digit: $4$ remaining choices; tens excludes the hundreds and units digits: $4$ remaining choices. Total per units digit $=4\times4=16$ ; over $3$ units choices $=3\times16=48$ . …

Start your 14-day free trial to unlock the full solution →

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2025Set ANNUAL1 markMCQ
$Q. The number of 5 digit numbers, all digits of which are odd is:$
(a) $5^6$
(b) $25$
(c) $625$
(d) $5^5$
›Reveal solutionSolution

Each of the 5 digit-positions is filled independently from the 5 odd digits.

The odd digits available are $\{1,3,5,7,9\}$ , a set of 5 digits. Since none of them is $0$ , there is no restriction on the leading digit either. Each of the 5 positions of the number can be filled in 5 ways, independ …

Start your 14-day free trial to see the full solution →
CBSE 2022Set ANNUAL1 markMCQ
$Q. The number of 5 digit numbers all digits of which are odd is:$
(a) $5^6$
(b) 25
(c) 625
(d) $5^5$
›Reveal solutionSolution

With 5 choices of odd digit for each of the 5 positions (no restriction, since all odd digits are already non-zero), the count is $5^5$ .

The odd digits are $1,3,5,7,9$ -- exactly 5 of them.

A 5-digit number has 5 positions, and unlike a general 5-digit number problem, there's no separate restriction on the leading digit here, because none of the allowed digits (odd digits) is zero anyway.

…

Start your 14-day free trial to see the full solution →
CBSE 2019Set ANNUAL1 markMCQ
$Q. The number of five digit numbers in which all digits are even, is:$
(a) $4\times 5^4$
(b) $4\times 5^5$
(c) $5^5$
(d) $5\times 5$
›Reveal solutionSolution

With digits restricted to $\{0,2,4,6,8\}$ , the first digit excludes 0 (4 choices) and the remaining 4 digits are unrestricted (5 choices each), giving $4\times 5^4$ .

The even digits available are $0, 2, 4, 6, 8$ — 5 digits in total, and repetition is allowed (the question only restricts which digits may be used, not that they be distinct).

For a 5-digit number, the first (leftmost) digit cannot be 0, so it has $5-1=4$ choices.

…

Start your 14-day free trial to see the full solution →

←Previous question · 4.3Q6 — How many numbers are there between 100 and 500 with the digits 0,1,2,3…→Next question · 4.3Q8 — Count the numbers between 999 and 10000 subject to the condition that …

Q.How many three-digit odd numbers can be formed by using the digits $0,1,2,3,4,5$ ? if

Concept understanding — Fundamental Principles of Counting

The Fundamental Principle of Counting

The Intuition: A Fork in the Road

The Precise Statement

A Simple Example

Q.How many three-digit odd numbers can be formed by using the digits 0,1,2,3,4,50,1,2,3,4,50,1,2,3,4,5? if

🎓Unlock everything free for 14 days

Q.How many three-digit odd numbers can be formed by using the digits $0,1,2,3,4,5$ ? if

Unlock everything free for 14 days