Your list · 0 हिं

Counting and Basic Probability · Question 22 of 65

Question 22

MediumOriginal question

How many diagonals does a polygon with 10 sides have?

35Correct answerYour answer45Correct answerYour answer70Correct answerYour answer90Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Any 2 of the 10 corners give a line segment: ${}^{10}C_{2} = 45$ .
10 of these segments are the sides, not diagonals.
Diagonals $= 45 - 10 = 35$ .

Worth noting

45 forgets to remove the sides. 70 is $10 \times 7$ , counting each diagonal from both ends.

Concept: Diagonals of a polygon as pairs of vertices minus sides
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsArrangements and selections

Practise this chapter →

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

Practise this chapter →

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

Practise this chapter All 65 questions in Counting and Basic Probability Revise the notes for Counting and Basic Probability