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Class 11 Permutations and Combinations worksheet
CBSE Mathematics. Counting principle, ⁿPᵣ and ⁿCᵣ, words, committees, selections. 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.
The value of ⁶P₃ is:
- 360
- 20
- 216
- 120
Answer
(d) 120
6 × 5 × 4
- 2.
The value of ¹⁵C₅ is:
- 360,360
- 5,005
- 3,003
- 2,002
Answer
(c) 3,003
15! ÷ (5! × 10!)
- 3.
How many arrangements can be made of all the letters of the word MISSISSIPPI?
- 69,300
- 17,325
- 39,916,800
- 34,650
Answer
(d) 34,650
11! ÷ (repeats: I × 4, S × 4, P × 2)
Section B · short answer
- 4.
How many arrangements of the letters of CLOUDY are there? How many of them begin with O?
Answer
720; 120
6!; fix O, then 5!
- 5.
How many 3-digit even numbers can be formed from the digits 1 to 7, if no digit is repeated?
Answer
90
units digit: 3 even choices; the rest: ⁶P₂
Section C · long answer
- 6.
(a) How many arrangements of the letters of TOMATO are there? (b) In how many of them do all the vowels come together?
Answer
(a) 180; (b) 36
(b) treat the vowels OAO as one block: 12 arrangements of the block and the consonants, × 3 arrangements of the vowels inside it
Fresh sheets for your child
In the app, every Permutations and Combinations 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.