07 Permutations and Combinations
Exercise 02
Question:
Evaluate (n−r)!/n!, when (i) n=6,r=2. (ii) n=9,r=5
Answer:
(i) (6-2)!/6! = (4!)/6! = (24)/720 = 0.0333
(ii) (9-5)!/9! = (4!)/9! = (24)/362880 = 0.000066
Question:
Evaluate (i) 8! ii) 4!−3!
Answer:
(i) 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
(ii) 4! - 3! = 4 x 3 x 2 x 1 - 3 x 2 x 1 = 4
Question:
Compute 8!/6!×2!
Answer:
- 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
- 6! = 6 × 5 × 4 × 3 × 2 × 1
- 8!/6! = 8 × 7 × 5 × 4 × 3 × 2 × 1
- 8!/6! × 2! = 8 × 7 × 5 × 4 × 3 × 2 × 1 × 2
- 8!/6! × 2! = 16 × 7 × 5 × 4 × 3 × 2 × 1
Question:
Is 3!+4!=7! ?
Answer:
Step 1: Calculate 3! 3! = 3 x 2 x 1 = 6
Step 2: Calculate 4! 4! = 4 x 3 x 2 x 1 = 24
Step 3: Calculate 7! 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
Step 4: Compare 3!+4! and 7! 3! + 4! = 6 + 24 = 30 7! = 5040
Therefore, 3!+4! ≠ 7!
Question:
If 1/6!+1/7!=x/8!, find x.
Answer:
Step 1: Calculate 1/6! 1/6! = 1/720
Step 2: Calculate 1/7! 1/7! = 1/5040
Step 3: Add 1/6! and 1/7! 1/6! + 1/7! = 1/720 + 1/5040
Step 4: Simplify the expression 1/6! + 1/7! = (720 + 5040)/5040
Step 5: Substitute the expression for x/8! x/8! = (720 + 5040)/5040
Step 6: Multiply both sides by 8! x/8!8! = (720 + 5040)/50408!
Step 7: Simplify x = (720 + 5040)*8
Step 8: Calculate x = 44160
Question:
Evaluate n!/(n−r)!, when. n=9,r=5.
Answer:
n!/(n-r)! = 9!/(9-5)! = 9!/(4!) = 98765!/(432*1) = 15120/24 = 630
JEE NCERT Solutions (Mathematics)
01 Sets
02 Relations and Functions
03 Trigonometric Functions
04 Principle of Mathematical Induction
05 Complex Numbers and Quadratic Equations
06 Linear Inequalities
07 Permutations and Combinations
08 Binomial Theorem
09 Sequences and Series
10 Straight Lines Exercise
10 Straight Lines Miscellaneous
11 Conic Sections
12 Introduction to Three Dimensional Geometry
13 Limits and Derivatives
14 Mathematical Reasoning
15 Statistics
16 Probability