Find the best tutors and institutes for Class 11 Tuition
Q5(ii):
Evaluate $frac{n!}{(n-r)!}$, when (ii) $n = 9, r = 5$.
Solution :
Step 1: Definition of Factorial and Permutation Formula
The expression provided is $\frac{n!}{(n-r)!}$, which mathematically represents the number of permutations of $n$ distinct objects taken $r$ at a time, denoted as $P(n, r)$. By definition, the factorial of a non-negative integer $n$ is the product of all positive integers less than or equal to $n$: $n! = n \times (n-1) \times (n-2) \times \dots \times 1$.
Step 2: Substitution of Given Values
Given the variables:
- $n = 9$
- $r = 5$
Step 3: Simplification of the Denominator
Perform the subtraction within the parentheses: $9 - 5 = 4$ Thus, the expression simplifies to: $$\frac{9!}{4!}$$
Step 4: Algebraic Expansion and Cancellation
Per the property of factorials $n! = n \times (n-1) \times \dots \times (k+1) \times k!$, we expand $9!$ until we reach $4!$ to facilitate the reduction of the fraction: $$\frac{9 \times 8 \times 7 \times 6 \times 5 \times 4!}{4!}$$ [By the definition of factorial division, common factors in the numerator and denominator can be cancelled provided the denominator is non-zero]. $$\text{Expression} = 9 \times 8 \times 7 \times 6 \times 5$$
Step 5: Final Computation
Executing the multiplication sequentially:
- $9 \times 8 = 72$
- $72 \times 7 = 504$
- $504 \times 6 = 3024$
- $3024 \times 5 = 15120$
Visualization of Permutation Logic
Final Solution: 15120
More Questions from Class 11 Mathematics Permutations and Combinations EXERCISE 6.2
CBSE Solutions for Class 11 Mathematics Permutations and Combinations
Chapters in CBSE - Class 11 Mathematics
Top Tutors who teach Permutations and Combinations
Super Tutor
Sector 15, New Chandigarh
13 yrs of
Exp
48 students
3170 hrs of classes completed
400
per hour
Online Classes
Go through my profile to know about me Chemistry 11 is a pivotal, often challenging, transition from general science to in-depth, analytical chemistry, focusing on atomic structure, stoichiometry, and chemical reactions. The experience involves intensive lab work, rigorous mathematical problem-solving (mole concept), and understanding molecular behavior, moving from conceptual understanding to practical, hands-on experimentation.
She was an excellent tutor; thanks to her guidance, I achieved outstanding marks in my 12th-grade board exams. Thank you is such a small word for all your help—thank you so much, Ma'am! ❤️✨
Super Tutor
Kasavanahalli Main Rd Kasavanahalli, Bangalore
2 yrs of
Exp
1 student
880 hrs of classes completed
800
per hour
Online Classes
I am a teacher. I love teaching and want to share my knowledge with my students. I will take online classes. My approach combines clear concepts, regular practice, and student-friendly strategies to make learning effective and enjoyable.
Super Tutor
H C Sarani, Kolkata
18 yrs of
Exp
8 students
2060 hrs of classes completed
500
per hour
Online Classes
Tutor's home
Students of 11th standard faces major challenges in three segments: 1) Boolean Algebra & Logic Gates 2) Developing the programming logic and 3) Database Management System 4) Java/ Python
Top Tutor
Anna Nagar Mullai Nagar, Chennai
9 yrs of
Exp
6 students
415 hrs of classes completed
600
per hour
Online Classes
Hi, I'm Kalaiselvi, an M.Sc. Mathematics graduate with 9 years of experience in one-on-one online Maths tutoring. I specialize in teaching Classes 10, 11, and 12 for CBSE and Tamil Nadu State Board. My classes are conducted in both English and Tamil (bilingual), making concepts easy to understand. I focus on concept clarity, problem-solving, regular practice, and exam preparation, with personalized attention for every student.
Great experience with Kalaiselvi Ma'am, her knowledge and skill on the subject are amazing. Thank you for your support and guidance.
Top Tutor
Vile Parle East, Mumbai
10 yrs of
Exp
5 students
201 hrs of classes completed
500
per hour
Online Classes
Tutor's home
Chemistry class 11 and cbse and state board free lance tutor online as well as teaching at my home
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Mathematics Permutations and Combinations EXERCISE 6.2 worksheets
Download Now
