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Question 1:

Evaluate

  1. 8!
  2.  4! – 3!

Question 2:

Is 3! + 4! = 7!?

Question 3:

Compute

8!/(6!X 2!)

Question 4:

Calculate x if

Question 5:

Evaluate,

n!/(n-r)!

when

 (i) n = 6, r = 2

(ii) n = 9, r = 5

 

Solution 1

We know that

n!=n(n-1)(n-2)……3*2*1

So solving the below questions based on that

 

  1. 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320
  2. First calculate  the factorials

    4! = 1 × 2 × 3 × 4 = 24

    3! = 1 × 2 × 3 = 6

    Then 4! – 3! = 24 – 6 = 18

Solution 2

We know that factorials is given by

n!=n(n-1)(n-2)……3*2*1

So solving the below questions based on that

 

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

So it is clear that

3! + 4! ≠ 7!

 

Solution 3

8!/(6!X 2!)

= 8*7 *6!/6! * 2

=8*7/2=28

Solution 4:

Solving this

x=64

Solution  5:

n!/(n-r)!

when

 (i) n = 6, r = 2

(ii) n = 9, r = 5

n!/(n-r)!= 6!/4!=30

n!/(n-r)!= 9!/4!=9*8*7*6*5=15120

 

 


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