Seven runners reach the final of a school 400 m race. In how many ways can the gold, silver and bronze medals be awarded, if no two runners tie?

35Correct answerYour answer210Correct answerYour answer343Correct answerYour answer5,040Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Gold can go to any of 7 runners, silver to any of the other 6, bronze to any of the remaining 5.
Ways $= 7 \times 6 \times 5 = {}^{7}P_{3} = 210$ .

Worth noting

35 is ${}^{7}C_{3}$ , which ignores which medal each runner gets. 343 is $7^3$ , which lets one runner win two medals.

Ten questions from Counting and Basic Probability, at your own pace.

Ten questions from Counting and Basic Probability, at your own pace.

Explanation