SOLUTION: From the numbers 1,2,3,4,5,6,7,8, and 9, four different numbers are selected to form a four-digit number. a.How much four-digit numbers can be formed? b.How many four-digit less

(a)  9 options for the most-left digit;

     8 remaining options for the next digit;

     7 remaining options for the next digit;

     6 options for the last digit.


     In all, there are  9*8*7*6 =  3024  such numbers.      ANSWER



(b)  " Less than 2000 "  means that the first digit is 1.


     Then there are 8 remaining options for the next digit;

                    7 remaining options for the next digit;

                    6 remaining options for the last digit.


     In all, there are  8*7*6 =  336  such numbers.       ANSWER




(c)  The last digit ("ones" digit) is any of four even digits 2, 4, 6 8, giving 4 options

     The "tens" digit is any of 8 remaining digits, giving 8 options;

     The "hundreds" digit is any of 7 remaining digits, giving 7 options;

     The "thousands" digit is any of 6 remaining digits, giving 6 options.


     In all, the number of options is  4*8*7*6 = 1344,  giving  1344 possible numbers.