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
