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Curated by: Khan Academy India - English (21 videos)
This video tackles the case where a digit is torn between two conflicting constraints. We try to make two digit numbers using a set of digits that include 0. We first solve for a case where repetition is allowed. We run into problems where repetition is not allowed - even though we are dealing with the last digit constraint. We quickly realise that the issue is not with the boxes but with the digit zero. We arrive at a neat solution involving cases and use it to solve another similar practice problem. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:permutations-and-combinations-ncert-new/xea4762213f311c5e:untitled-900/e/permutations_1) Timestamps: 00:00 Problem 1 (Find all even numbers, 0 is one of the digits) 00:21 Solution 1 (repetition is allowed) 01:53 Problem 2 (Same digits, repetition not allowed) 02:03 Attempt 1 (taking no even values) 02:34 Comparing result with actual 02:57 Attempt 2 (taking one even value) 03:28 Comparing result with actual 03:50 Breaking down the issue with 0 04:18 Separating the lists through cases 05:12 Solving case 1 (last digit zero) 05:33 Solving case 2 (last digit non zero) 06:15 Practice problem 2 (3 digit even numbers) 06:44 Solving case 1 (last digit zero) 07:17 Solving case 2 (last digit non zero) 08:33 Adding results from both cases Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Ashish Gupta