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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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Prove that : (i) ""^(n)P_(n)=2""^(n)P_(n-2) (ii) ""^(10)P_(3)=""^(9)P_(3)+3""^(9)P_(2) .

Show that ""^(n)P_(n)=""^(n)P_(n-1) for all natural numbers n.

2.^(n)P_(3)=^(n+1)P_(3)

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

If show that "^(n-1)P_r = (n-r).^(n-1)P_(r-1)

Let ."""^(n)P_(r) denote the number of permutations of n different things taken r at a time . Then , prove that 1+1."""^1P_(1) + 2 ."""^(2)P_(2) + 3."""^(3)P_(3) +.....+ n . """^(n)P_(n) = . """^(n+1)P_(n+1)

Find 'n' if : (i) ""^(2n)P_(3)=100 ""^(n)P_(2) (ii) ""^(n)P_(4)=20xx ""^(n)P_(2)

If ""^(n)P_(4) =2xx""^(5)P_(3) , find n.

Find 'n' if 2 ""^(5)P_(3)= ""^(n)P_(4)

AAKASH INSTITUTE-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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