Last updated at Dec. 24, 2019 by Teachoo
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Ex 7.3, 3 (Method 1) How many 3digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated? We need to find 3 digit even number using 1, 2, 3, 4, 6, 7, Hence units place can have either 2, 4 or 6 Number of even numbers if 2 is at units place Hence these are 5 more digits left (1, 3, 4, 6, 7) for Hence n = 5 which we need to fill 2 place and r = 2 Number of 3 digit even number with 2 at unit place = nPr = 5P2 = 5!/((5 − 2)!) = 5!/3! = (5 × 4 × 3!)/3! = 20 Thus, Number of 3 digit even number with 2 at unit place = 20 Similarly Number of 3 digit can number with 4 at unit place = 20 and 6 at unit place = 20 Hence, Total 3digit even numbers = 20 + 20 + 20 = 60 Ex 7.3, 3 (Method 2) How many 3digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated? Let the 3 digit even number be Only 3 numbers are possible at units place (2 , 4 & 6) as we need even number. Number of 3 digit even numbers = 3 × 5 × 4 = 60
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Digits: 1, 2, 3, 4, 5 Q: how many even 3 digit numbers can be made without repeating them? In total, I worked out that there's 60 three digit numbers that can be made without repeating (5C1 x 4C1 x 3C1) = 60. But, I have no idea about the even bit. Could somebody talk me through it so I can understand? Thanks!
$\endgroup$ 1 In mathematics, permutation is known as the process of arranging a set in which all the members of a set are arranged into some series or order. The process of permuting is known as the rearranging of its components if the set is already arranged. Permutations take place, in more or less important ways, in almost every area of mathematics. They frequently appear when different commands on certain finite sets are considered. What is a Combination? A combination is an act of choosing items from a group, such that (not like permutation) the order of choice does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the union of n things taken k at a time without repetition. In combination, you can select the items in any order. To those combinations in which reoccurrence is allowed, the terms kselection or kcombination with replication are frequently used. Permutation Formula In permutation r things are selected from a set of n things without any replacement. In this order of selection matter.
Combination Formula In combination r things are selected from a set of n things and where the order of selection does not matter.
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Similar QuestionsQuestion 1: How many 3 digit odd numbers can be formed by using the digits 1,2,3,4 and 5? Solution:
Question 2: How many 4 digit even numbers can be formed by using the digits 1,2,3,4 and 5? Solution:
