Total letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !

Correct Option: D

Total letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2 ! ] / 2 ! = 2520

Required number of arrangements = 6 ! / 3 ! [∵ S has come thrice ]

Correct Option: D

Required number of arrangements = 6 ! / 3 ! [∵ S has come thrice ]
= [ 6 x 5 x 4 x 3! ] /3 !
= 120

Number of arrangements n ! /( p ! q ! r ! )
Total letters = 6, but R has come twice.
So, required number of arrangements
= 6 ! / 2 !

Correct Option: E

Number of arrangements n ! /( p ! q ! r ! )
Total letters = 6, but R has come twice.
So, required number of arrangements
= 6 ! / 2 ! = (6 x 5 x 4 x 3 x 2 !) / 2 ! = 360

The word 'INHALE' has 6 distinct letters.
∴ Number of arrangements = n !

Correct Option: A

The word 'INHALE' has 6 distinct letters.
∴ Number of arrangements = n ! = 6 !
= 6 x 5 x 4 x 3 x 2 x 1
= 720

∵ ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1
⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)

Correct Option: B

∵ ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1
⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)
⇒ 56 x 55 = 30800/(51 - r)
⇒ 51 - r = 10
∴ r = 41