Question

In how many ways can the letters of the word PERMUTATIONS be arranged if there are always 4 letters between P and S

Answer 1

Answer:

Step-by-step explanation:

In how many ways can the letters of the word- PERMUTATIONS be arranged if there are always 4 letters between P and S. Answer: There are 12 letters in which T is repeated twice. We need to select 4 letters between P and S from 10 letters in 10C4 = 210 different ways.

Answer 2

Yups.
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P ERMUTATIONS
P,E,RM,U,TT,A,I,ON,S
since P and S can be arranged in 7 ways as u can see beloW
P ∆ ∆ ∆ ∆ S ∆ ∆ ∆ ∆∆∆∆∆
∆P∆∆∆∆S∆∆∆∆∆
∆∆P∆∆∆∆S∆∆∆∆
∆∆∆P∆∆∆∆S∆∆∆
∆∆∆∆P∆∆∆∆S∆∆
∆∆∆∆∆P∆∆∆∆S∆
∆∆∆∆∆∆P∆∆∆∆S
as P and S can also exchange there places so 7×2
Now ,
there are left 10 empty places , we need fit them,
10!/2!
2! becoz there are 2T's
now 10!/2! × 7 ×2
so this is the answer