Combinatorics Worksheet

You may want to read Permutations and Combinations and combinatorics before doing this worksheet. Note that I originally wrote this worksheet for a Canadian audience; a "loonie" is a $1 coin and a "toonie" is a $2 coin. "Lottario" was a lottery that was held in Ontario at the time.

• A penny, a nickel, a dime, a quarter, a loonie, and a toonie are flipped. How many possible outcomes are there?
• How many three-digit numbers are there such that all three digits are divisible by three?
• Calculate the number of arrangements of the letters of the word "mathematics" if:
  • All combinations are valid.
  • The two M's are side-by-side.
  • All of the vowels are at the start of the arrangement.
• In how many ways can three cards be selected at random from a deck of cards?
• In Lottario, six numbers are drawn from a pool of 45. How many different combinations of six winning numbers are there?
• How many five-person committees can be selected from six men and eight women if there must be at least two women included?