   SEARCH HOME Math Central Quandaries & Queries  Question from Spence, a parent: My son has a problem that he has been unable to figure out. I was asked to try, but I am confused on how to get the last two parts. Any help would be great. Thanks Spence How many four-digit numbers can be formed under each condition? A) The leading digit cannot be zero: 9(10)(10)(10)=9000 B) The leading digit cannot be zero and no repetition of digits allowed: 9(9)(8)(7)=4536 C) The leading digit cannot be zero and the number must be less than 5000: ?? D) The leading digit cannot be zero and the number must be even: ?? Hi Spence,

C) is very much like A) with the one difference that the number must be less than 5000 so the only choices for the first digit are 1, 2, 3 and 4.

D) again is similar to A) but the to be even the last digit must be even. Thus the last digit must be 0, 2, 4, 6 or 8.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.