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 June 29th, 2019, 02:00 AM #1 Newbie   Joined: Jun 2019 From: n yutu Posts: 2 Thanks: 0 hOW TO SOLVE THIS Hello sir, How to solve this? The number of even numbers of three digit which can be formed with digit 0,1,2,3,4 and 5 (no digit can be used more than once) is 1. 60 2. 92 3. 52 4. 48 Last edited by skipjack; July 1st, 2019 at 02:30 PM.
 June 29th, 2019, 09:08 AM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 309 Thanks: 160 Even number, so the third digit must be 0, 2, or 4 (three possibilities). Second digit must be one of the five remaining digits. First digit must be one of the four remaining. Does that help? Thanks from topsquark
 June 29th, 2019, 10:35 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra That doesn't account for the zero in the first place.
 June 29th, 2019, 10:51 AM #4 Senior Member     Joined: Sep 2015 From: USA Posts: 2,585 Thanks: 1430 Last digit is always even, i.e. 0, 2, 4 Assume first digit is even. There are 2 ways to assign the first digit, and 2 ways to assign the last digit. Then having assigned these there are 4 ways to assign the 2nd digit. This is a total of 16 numbers. Assume the first digit is odd. There are 3 ways to assign the first digit, 3 ways to assign the last digit. Then there are 4 ways to assign the 2nd digit. This is a total of 36 36+16 = 52 Thanks from skeeter
 June 30th, 2019, 06:15 AM #5 Math Team     Joined: Jul 2011 From: Texas Posts: 3,034 Thanks: 1621 digit choices ... Odd, Odd, Even $3 \cdot 2 \cdot 3 = 18$ Odd, Even, Even $3 \cdot 3 \cdot 2 = 18$ Even, Odd, Even $2 \cdot 3 \cdot 2 = 12$ Even, Even, Even $2 \cdot 2 \cdot 1 = 4$
 July 1st, 2019, 02:41 PM #6 Global Moderator   Joined: Dec 2006 Posts: 21,029 Thanks: 2259 There are 5 × 4 = 20 3-digit numbers that end in 0. There are similarly 20 that end in 2 and 20 that end in 4, making 60 in total. If, however, numbers that have a leading zero are excluded, the 8 numbers 012, 014, 024, 032, 034, 042, 052 and 054 are excluded. and so the total is 60 - 8 = 52.

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