Counting Pre-Test

Count with the clown

(1) 7 teams compete in a men’s hockey league. If each team plays each other twice, how many games are necessary to complete the league schedule?

(a) 42 (b) 21 (c) 84 (d) 52

(2) The sum of the seventh row of Pascal’s triangle is the same solution to;

(a) The number of solutions a student could get if they guessed on six questions of a multiple choice exam, each question having four answers.

(b) The number of solutions a student could get if they guessed on six questions of a true false exam.

(c) The number of solutions a student could get if they guessed on seven questions of a multiple choice exam, each question having four answers.

(d) The number of solutions a student could get if they guessed on seven questions of a true false exam.

(3) Eight friends go to dinner. How many ways can they be seated at a circular table if three of them insist on sitting together?

(4) A multiple choice exam has 20 questions, each with four possible answers, and 10 additional questions, each with five possible answers. How many different answer sheets are possible?

(5) In a 52 card deck, how many 5 card poker hands are possible that have exactly two pair? one pair?