A 4-digit number is selected at random formed by using the digits and (where repetition of digits is not allowed) What is the probability that the number selected is divisible by ? अंकों 0, 1, 2, 3 और 4 का उपयोग करके गठित की गई एक 4- अंकीय संख्या यदृच्छया चुनी जाती है। (जहाँ अंकों की पुनरावृत्ति की अनुमति नहीं है) । चुनी गई संख्या 6 से विभाज्य है , की प्रायिकता क्या है ?

Explanation: 1. Calculate Total Sample Space ( ): The total number of 4-digit numbers that can be formed using the set without repetition is . 2. Condition for Divisibility by 6: A number is divisible by if it is divisible by both and . Divisibility by : The number must be even (last digit ). Divisibility by : The sum of the digits must be divisible by . 3. Analyze Digit Subsets (Sum must be ): We select 4 digits out of 5 such that their sum is divisible by . Total sum of is . Case A: Exclude (Sum ): Digits . Numbers must be even (last digit ). Ends in : numbers. Ends in : First digit numbers. Ends in : First digit numbers. Total for Case A . Case B: Exclude (Sum ): Digits . Ends in : numbers. Ends in : First digit numbers. Total for Case B . 4. Final Probability Calculation: Total favorable outcomes .

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

A 4-digit number is selected at random formed by using the digits $0, 1, 2, 3,$ and $4$ (where repetition of digits is not allowed)

What is the probability that the number selected is divisible by $6$ ?

अंकों 0, 1, 2, 3 और 4 का उपयोग करके गठित की गई एक 4-अंकीय संख्या यदृच्छया चुनी जाती है। (जहाँ अंकों की पुनरावृत्ति की अनुमति नहीं है) ।

चुनी गई संख्या 6 से विभाज्य है, की प्रायिकता क्या है ?

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