Combinatorics Word Problem! Answer CHECK

Answer Check...

27. b) Question: **In how many ways can a president, vice-president, and treasurer be chosen from an organization with 12 members?**

My answer:

C (12, 3) = 12! divided by 4! 3! = 3,326,400 different ways?

28. a) Question: **How many 4-digit #'s can be formed from the set A = {0,1,2,3,4,5,6} if there is no repetition? (**NOTE: 0123 is not a 4-digit number because it equals 123)**

My answer:

You can choose the 4 digits from set A in (7 4) ways.

# of digits = 7! ÷ 4! 3! x 4! -1

= 840-1

= 839

* You subtract 1 to represent the 0123 4-digit number that would form (which doesn't count)

b) Question: **How many of the numbers in part a) are odd?**

My answer:

Because we are selecting odd #'s only - there are just 5 choices for the last digit (1,3,5,7,9)

Number of odd digits = 8 x 8 x 7 x 5

= 2240 different odd numbers

c) Question: **How many of the numbers in part a) contain a 3?**

**My answer: ?? DON't KNOW!!**