SOLUTION: How many 3 digit numbers can be formed from 1,2,3,4,5,6 if a) repition is allowed b) the number MUST be odd and no repetition is allowed c) the number MUST be less than 300 and

Algebra ->  Permutations -> SOLUTION: How many 3 digit numbers can be formed from 1,2,3,4,5,6 if a) repition is allowed b) the number MUST be odd and no repetition is allowed c) the number MUST be less than 300 and       Log On


   

Question 848561: How many 3 digit numbers can be formed from 1,2,3,4,5,6 if
a) repition is allowed
b) the number MUST be odd and no repetition is allowed
c) the number MUST be less than 300 and no repition is allowed
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
a) If repetition is allowed, this is a form of with replacement. We can calculate this pretty easily. In short, there is 6^3 (216) ways to do this because for each number we place, there are 6 numbers that we can use.
b) Here this is considered without replacement. After the use of a digit, it no longer is a possible option for the next digit. So we have 6*5*4= 120 This commonly represented as 6P3.
c) Notice our first digit is now only limited to 1 and 2. So there is only 2 numbers that satisfy our first digit. Our second digit only has 5 possible digits. Our third digit only has 4 numbers that can satisfy it.
So 2*5*4 = 40 numbers