Math Homework Help!! Permutations, Combinations, Factorial, Counting Techniques

Question

1. Suppose there are 6 horses running in a race. How many different outcomes (orderings from first to sixth place) are possible? Ignore the possibility of ties.

2. In a Lotto game, a player must choose 6 different numbers between 1 and 42. The order of the numbers is not important. In how many ways can a player do this?

3. A multiple choice test consists of 12 questions with 4 possible answers to each question. In how many ways can the test be completed?

4. Suppose a bank password must consist of 5 digits or letters (they can be mixed).
a) How many such passwords are possible? b) How many such passwords begin with the letter B?

Answer 1

1)  6!         2)₄₂C₆ (I ASSUME YOU'LL EVALUATE ON A CALCULATOR)   3)  4¹² = 2²⁴ = 16,777,216

 

4)  a) 36⁵ because each of 5 characters can be assigned any of the 36 symbols (26 letters, 10 digits)

     b) 36⁴