Ex 7.3, 3 (Method 1) How many 3-digit 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 3-digit even numbers = 20 + 20 + 20 = 60 Ex 7.3, 3 (Method 2) How many 3-digit 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 Show Solution : total number of digits = 6 Ex 7.1, 2 How many 3 digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Let the 3 digit even number be Only 3 numbers are possible at units place (2 , 4 & 6) as we need even number. But at tens & hundreds place all 6 are possible Number of 3 digit even numbers = 3 × 6 × 6 = 108 Rough 158 is even as 8 is even 296 is even as 6 is even Show MorekingW3 answer is absolutely correct. I'm not debating on his answer, just answering in the way the question has been asked.
Therefore we get, 3C1 x 4C1 x 2C1 = 24 The thing you have done How many 3Thus, by multiplication principle, the required number of 3-digit numbers is 3×20=60.
How many 3Thus, 3-digit even number can be formed in 108 ways.
How many 3So, number of ways in which three digit even numbers can be formed from the given digits is 6×6×3=108.
How many 3so , ans=3*5*4=60. Q.
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