SOLUTION: How many positive even 10 digit numbers can be written using 7 ones and 3 zeroes ?thanks for any help .

The leftmost position digit can not be 0 --- hence, it is 1, since there is no other possibilities.


The rightmost position (the "ones" position) must be 0 to provide an even number.


Hence, you have 8 remaining positions to fill with six ones and two zeros by an arbitrary way.


You can place two digits of zero among 8 positions by   =  different ways = 4*7 = 28 different ways,


It gives you 28 different 10-digit numbers  under the question.    ANSWER