Which of the following are true of false? (i) (2 + 3) ! = 2 ! + 3! (

1.	Which of the following are true of false? (i) (2 + 3) ! = 2 ! + 3! (ii) (2 × 3)! = (2!) × (3!)
Answer» Option (i) and (ii) both are false Proofs : For option (i), L.H.S. = (2 + 3)! = (5!) = 120 R.H.S. = (2!) + (3!) = 2 + 6 = 8 ∴ L.H.S. ≠R.H.S. For option (ii), L.H.S. = (2 × 3)! = (6!) = 720 R.H.S = (2!) × (3!) = 4 × 6 = 24 ∴L.H.S. ≠R.H.S. Important Notes : for any two whole numbers a and b, (a+b)! ≠ (a!) + (b!) (axb)! ≠ (a!) x (b!)

Which of the following are true of false? (i) (2 + 3) ! = 2 ! + 3! (ii) (2 × 3)! = (2!) × (3!)

Answer»

Option (i) and (ii) both are false

Proofs :

For option (i),

L.H.S. = (2 + 3)! = (5!) = 120

R.H.S. = (2!) + (3!) = 2 + 6 = 8

∴ L.H.S. ≠R.H.S.

For option (ii),

L.H.S. = (2 × 3)! = (6!) = 720

R.H.S = (2!) × (3!) = 4 × 6 = 24

∴L.H.S. ≠R.H.S.

Important Notes : for any two whole numbers a and b,

(a+b)! ≠ (a!) + (b!)

(axb)! ≠ (a!) x (b!)