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Show that ""^(n)P(n)=2""^(n)P(n-2)...

Show that
`""^(n)P_(n)=2""^(n)P_(n-2)`

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Explore conceptually related problems

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

Find the value of n such that "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.

Show that ""^(n)P_r =""^(n-1) P_r + r, ^(n-1) P_(r-1) Where the symbols have their usual meanings.

Prove that: (i) (.^(n)P_(r))/(.^(n)P_(r-2)) = (n-r+1) (n-r+2)

The value of n, if ""^(n)P_(5) = 20.""^(n)P_(3) , is

Find n, if ""^(n)P_(5)=42 ""^(n)P_(3), n ge 5

Find n if : "" ^(2n)P_(n+1) : ""^(2n-2) P_n = 56 : 3

Find n if : ""^(2n+1) P_(n-1) : ""^(2n-1) P_n = 3: 5

If ""^(2n-1)P_(n): ""^(2n+1)P_(n-1)=22:7 , find n.

If "^(n+5)P_(n+1) = (11(n-1))/2"^(n+3)P_n , find ndot

AAKASH INSTITUTE ENGLISH-PERMUTATIONS AND COMBINATIONS -Try Yourself
  1. Evaluate ""^(5)P(3)xx""^(7)P(3)

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  2. Find n, if ""^(n)P(5)=42 ""^(n)P(3), n ge 5

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  3. Show that ""^(n)P(n)=2""^(n)P(n-2)

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  4. In how many ways, the letter of word NUMBER can be arranged ?

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  5. In how many ways, the letters of word FRACTION can be arranged ?

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  6. How many numbers lying between 100 and 1000 can be formed with the dig...

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  7. How many four digit numbers are there in all?

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  8. How many permulations of the letters of the word KARNAL are there ?

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  9. How many words can be formed using the letters E twice , the letter C ...

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  10. Find the number of words formed by permuting all letters of the word I...

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  11. Find the number of different words formed with the letters of the word...

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  12. How many permutations can be made out of the letters of the word TRIAN...

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  13. Find out number of permutations that can be had from the letters of th...

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  14. How many numbers greater than 50,000 can be formed by using the digits...

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  15. How many numbers greater than a million can be formed by using the dig...

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  16. In how many ways can the letters of the word INSURANCE be arranged , s...

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  17. In how many ways can the letters of the word PATLIPUTRA be arranged, s...

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  18. The letters of word ZENITH are written in all possible ways. If all ...

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  19. If all the permutations of the lettters of the word INDIA are arranged...

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  20. Evaluate : ""^(75)C(73)

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