標題: [Core] 5** Maths Question of the Day 2.1 (DSE數學奪5**必做題型!!!) [已附答案] [打印本頁] 作者: whyalwaysme 時間: 2012-5-25 11:12 PM 標題: 5** Maths Question of the Day 2.1 (DSE數學奪5**必做題型!!!) [已附答案]
How many ways are there for sum of 3 numbers selected from 1 to 30 to be divisible by 3?
重要聲明:以後,If there are any discrepancies between the Chinese and English version, always refer the english version as the accurate one. 作者: blazehaze 時間: 2012-5-25 11:48 PM
Divide the numbers into three groups :
G1 : 1, 4, 7, ..., 28 (each number give a remainder 1 when it is divided by 3)
G2 : 2, 5, 8, ..., 29 (each number give a remainder 2 when it is divided by 3)
G3 : 3, 6, 9, ..., 30 (each number give a remainder 0 when it is divided by 3)
Case (i) : choose 3 numbers from G1, number ways = 10C3 = 120
Case (ii) : choose 3 numbers from G2, number ways = 10C3 = 120
Case (iii) : choose 3 numbers from G3, number ways = 10C3 = 120
Case (iv) ; choose a number from each group, number ways = 10x10x10 = 1000
Total number of ways = 120 + 120 + 120 + 1000 = 1360 作者: taifoo888 時間: 2012-6-21 09:29 PM
作者: shing1209 時間: 2012-7-1 07:09 PM
10C3 + 10C3 + 10C3 + 10x10x10 = 1360
dont know the ans of the second question. 作者: mk999317 時間: 2012-7-1 09:30 PM