回复:数学题求救,先谢了

来源: 2012-04-12 09:52:51 [博客] [旧帖] [给我悄悄话] 本文已被阅读:

The first question to answer is: how many 7 digit numbers are possible in base 10.

if zero cannot be used in the first position and all digits can repeat in the number, then there are 9 * 10 * 10 * 10 * 10 * 10 * 10 possible numbers.

if zero can be used in the first position and all digits can repeat in the number, then there are 10 * 10 * 10 * 10 * 10 * 10 * 10 possible numbers.

if zero cannot be used in the first position and no digits can repeat in the number, then there are 9 * 9 * 8 * 7 * 6 * 5 * 4 possible numbers.

if zero can be used in the first position and no digits can repeat in the number, then there are 10 * 9 * 8 * 7 * 6 * 5 * 4 possible numbers.

for the question being asked, where 1 digit can repeat exactly 4 times and zero can be used in the first position, then there would be 10 * 10 * 10 * 10 * 9 * 8 * 7 possible numbers.

when 2 digits can repeat exactly twice and zero can be used in the first position, then there would be 10 * 10 * 9 * 9 * 8 * 7 * 6 possible numbers.