NCERT Solutions for Class 11 Maths chapter-7 Permutation And Combination Exercise 7.2
NCERT Solutions for Class-11 Maths Chapter-7 Permutation and Combination
NCERT Solutions For Class 11 Maths Chapter-7 Permutation and Combination prepared by the expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download solution of all chapters from Physics Wallah NCERT solutions of class 11.
NCERT Solutions for Class-11 Maths Exercise 7.2
Question 1. Evaluate:
(i) 8!
(ii) (ii) 4! – 3!
Solution :
(i) 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320
(ii) 4! = 1 × 2 × 3 × 4 = 24
3! = 1 × 2 × 3 = 6
∴4! – 3! = 24 – 6 = 18
Question 2.Is 3! + 4! = 7!?
Solution :
3! = 1 × 2 × 3 = 6
4! = 1 × 2 × 3 × 4 = 24
∴3! + 4! = 6 + 24 = 30
7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040
∴ 3! + 4! ≠ 7!
Question 3. Compute 8! / 6! × 2!
Solution :
The product of the first n natural numbers is n factorial, which is written as n! and is given by, n!=n×(n−1)!
.
First consider the expression in the numerator, that is, 8!
.
According to the definition of the factorial,
8! = 8×(8−1)!
8! = 8×7!
This is further evaluated as,
8! = 8×7×6!
Now, consider the expression in the denominator, that is, 6!×2!
.
This expression can also be written in a way that is, 6!×2×1
.
Consider the expression that is to be determined and evaluated.
8!
/
6!×2!=8×7×6!
/
6!×2×1
8!
/
6!×2! = 8×72
8! / 6!×2!=28
Therefore, the value of the expression given on evaluation is found to be 28.
Question 4. If 1/6! + 1/7! = x/8!, find x
Solution :
Given: The product of the first n natural numbers is n factorial, which is written as n! and is given by,
Question 5. Evaluate n! / (n−r)!,
when
(i) n=6, r=2 (ii) n=9 ,r=5
Solution :
(i) Given: n=6, and r=2
(ii) Given: n = 9 and r = 5
