Vidaara.orgClass 11 · Mathematics
CodeVID-M11-06-FPC-01
Counting Principle & Factorial — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$4!=$
- A.$12$
- B.$24$
- C.$16$
- D.$8$
2.
$0!=$
- A.$0$
- B.$1$
- C.$\infty$
- D.undefined
3.
By the FPC, $m$ ways then $n$ ways gives:
- A.$m+n$
- B.$m\times n$
- C.$m^n$
- D.$m-n$
4.
$\dfrac{6!}{4!}=$
- A.$30$
- B.$24$
- C.$15$
- D.$720$
5.
The number of $2$-digit numbers from $\{1,2,3\}$ (repetition allowed) is:
- A.$6$
- B.$9$
- C.$3$
- D.$12$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $5!$.
7.
Evaluate $\dfrac{6!}{4!\,2!}$.
8.
How many $3$-letter words (repetition allowed) can be formed from $5$ letters?
9.
Simplify $\dfrac{n!}{(n-1)!}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
How many $3$-digit numbers can be formed from the digits $1$–$5$ without repetition?
11.
Find $n$ if $n!=720$.
12.
In how many ways can $4$ people sit in $4$ chairs?
13.
How many even $3$-digit numbers can be formed from $\{1,2,3,4,5\}$ without repetition?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
How many numbers between $100$ and $1000$ have all distinct digits?
15.
How many $4$-digit numbers can be formed using digits $0$–$9$ without repetition (no leading zero)?
Answer Key
Section A — Multiple Choice Questions
- (B) $24$
- (B) $1$
- (B) $m\times n$
- (A) $30$
- (B) $9$
Section B — Short Answer (2 marks)
- $120$.
- $15$.
- $125$.
- $n$.
Section C — Short Answer (3 marks)
- $60$.
- $n=6$.
- $24$.
- $24$.
Section D — Long Answer (5 marks)
- $648$.
- $4536$.
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