### 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)/5040*8!

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!) =
9*8*7*6*5!/(4*3*2*1) =
15120/24 = 630