Question-1 :-  Evaluate:
(i) 8 !
(ii) 4 ! – 3 !

(i) 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320 
(ii) 4! = 1 × 2 × 3 × 4 = 24
     3! = 1 × 2 × 3 = 6 
  Therefore,  4! – 3! = 24 – 6 = 18
   

Question-2 :-  Is 3 ! + 4 ! = 7 ! ?

  3! = 1 × 2 × 3 = 6
  4! = 1 × 2 × 3 × 4 = 24 
  Therefore, 3! + 4! = 6 + 24 = 30

  Now, 7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040 
  Therefore, 3! + 4! ≠ 7!
   

Question-3 :-  Compute: 8!/6!2! .

  8!/6!2!
= (8 x 7 x 6!)/(6! x 2 x 1)
= (8 x 7)/2
= 4 x 7
= 28
   

Question-4 :-  If 1/6! + 1/7! = x/8!, find x.

  1/6! + 1/7! = x/8!
  1/6! + 1/(7 x 6!) = x/(8 x 7 x 6!)
  1 + 1/7 = x/56
  8/7 = x/56
  x = (8 x 56)/7
  x = 8 x 8
  x = 64
   

Question-5 :-  Evaluate n!/(n-r)! , when
(i) n = 6, r = 2
(ii) n = 9, r = 5.

(i) When, n = 6, r = 2
  n!/(n-r)!
= 6!/(6-2)!
= 6!/4!
= (6 x 5 x 4!)/4!
= 6 x 5
= 30
  

(ii) When, n = 9, r = 5
  n!/(n-r)!
= 9!/(9-5)!
= 9!/4!
= (9 x 8 x 7 x 6 x 5 x 4!)/4!
= 9 x 8 x 7 x 6 x 5
= 15120