Find all possible arrangements of words given in (i) to (vi)

i. Given word is " PERMUTATION"

ii. "MATHEMATICS"

III. INDEPENDENCE

IV CORRUPTION

V. INTERMEDIATE

VI. COMBINATION

i. It contains 11 letters in which 2 T's, are alike and rest are different

Req. no. of arrangements $=\frac{11!}{2!}$

ii. It contains 11 letters in which 2 M's, 2 A's, 2 T's are alike and rest are different

Req. no. of arrangements $=\frac{11!}{2!2!2!}$

iii. It contains 12 letters in which there are 3 N's, 2 D's 4 E's are 

$\therefore$Req. no. of arrangements = $=\frac{12!}{3!2!4!}$

iv. It contains 10 letters in which there are 2 R’s, 2 O’s,  are alike and rest are different
Req. no. of arrangements $=\frac{10!}{2!2!}$

v. It contains 12 letters in which there are 2 I’s, 3 E’s, 2 T’s are alike and rest are different
Req. no. of arrangements $=\frac{12!}{2!.3!.2!}$

vi.It contains 11 letters in which there are 2 O’s, 2 I’s, 2 N’s are alike and rest and rest are different
Req. no. of arrangements $=\frac{11!}{{\left(2!\right)}^3}$