20點!!! F.6 M&S 急問

a)The 1st digit including 0 numbers - The numbers with 0 as the 1st digit= 7P4 - 6P3= 840 - 120= 720 different numbers.b)For the last digit is 0 ,The 1st , 2nd , 3rd digits can be any numbers of 1 , 2 , 5 , 6 , 7 , 8
6P3 = 120 casesFor the last digit is 2 , 6 or 8 ,The 1st digit have 5 cases since 0 cann't be the 1st digit ,
The 2nd digit have 5 cases ,
The 3rd digit have 4 cases ,
The last digit have 3 cases (2 , 6 or 8)
5x5x4x3 = 300 cases120 + 300 = 420 numbers formed in (a) are even.c)The sum of all numbers including the 1st digits is 0 :Each number appeared 6P3 = 120 times in each digit position , the sum= (0 + 1 + 2 + 5 + 6 + 7 + 8) x (1000 + 100 + 10 + 1) x 6P3= 29 x 1111 x 120 = 3866280The sum of numbers with 0 as the 1st digit :the sum = (1 + 2 + 5 + 6 + 7 + 8) x (100 + 10 + 1) x 5P2= 29 x 111 x 20 = 64380The sum of all numbers formed in (a) = 3866280 - 64380 = 3801900