How many different 10-digit numbers, such as 7,829,034,651, can be written by using all 10 digits? Numbers starting with zero are excluded.

Answer:

Ten digits can be permuted in 10! = 3,628,800 different ways. A 10-digit number cannot start with zero, so that we must subtract 3,628,800/10 = 362,880 to obtain the answer: 3,265,920.