Worksheets › Class 9 › Combinatorics (Advanced)
Class 9 · Mathematics worksheetCombinatorics (Advanced)
CBSE Mathematics. Optional Advanced level: counting principle, factorials, permutations and combinations, digits, words, committees and points. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
In a race of 6 runners, in how many ways can Gold, Silver and Bronze be awarded (no ties)?
- 216
- 20
- 30
- 120
Answer
(d) 120
⁶P₃ = 6 × 5 × 4
- 2.
In how many ways can a panel of 5 be chosen from 15 people?
- 75
- 1,365
- 3,003
- 360,360
Answer
(c) 3,003
¹⁵C₅ = 360,360 ÷ 5!
- 3.
0! is taken to be:
- 10
- −1
- 0
- 1
Answer
(d) 1
so that formulas like ⁿCₙ = n! ÷ (n! × 0!) = 1 work
Section B · short answer
- 4.
Find x if 1/8! − 1/9! = x/10!.
Answer
x = 80
multiply by 10!: x = 10 × 9 − 10 = 80
- 5.
How many 5-letter words (with or without meaning) can be formed from the letters of PLANET if no letter is repeated?
Answer
720
PLANET has 6 different letters: ⁶P₅ = 6 × 5 × 4 × 3 × 2
Section C · long answer
- 6.
A committee of 5 is to be chosen from 8 men and 5 women so that it has at least 4 women. In how many ways can this be done?
Answer
41
⁵C₄ × ⁸C₁ + ⁵C₅ × ⁸C₀
Fresh sheets for your child
In the app, every Combinatorics (Advanced) sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.