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There are always 4 letters between P and S?

Question

There are always $4$ letters between $P$ and $S$ ?

25401600

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Evelyn Discussed

There are always

4

letters between

P

and

S

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

There are

12

letters in word

PERM U T A T I ONS

T

occurs twice .
Here,

P

and

S

are fixed. These

P

and

S

can interchange their position. Hence,

P

and

S

can be arranged in

2!

ways.
Since,

P

and

S

are fixed, there are

10

letters left , where

T

occurs twice .
From these

10

letters,

4

letters can be chosen in

\frac{^{10} C _{4}}{2 !}

ways.
Now since,

4

letters are between

P

and

S

, so these six letters can be considered as a single object (letter). These four letter (between

P

and

S

)can be arranged in

4!

ways.
Now, the remaining

6

letters and 1 object i.e. total

7

can be arranged in

7!

ways.
Hence, required number of ways

= 2! \frac{^{10} C _{4}}{2 !} 4! 7!

= 25401600

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Question Text	There are always $4$ letters between $P$ and $S$ ?
Answer Type	Text solution:1
Upvotes	151

There are always 4 letters between P and S?

Text solutionVerified

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There are always $4$ letters between $P$ and $S$ ?