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Evaluate "(i) "^(12)P(4) " (ii)...

Evaluate
`"(i) "^(12)P_(4) " (ii) "^(75)P_(2) " (iii) "^(8)P_(8)`

Text Solution

Verified by Experts

` "(i) "^(12)P_(4)=(12!)/((12-4)!)=(12!)/(8!)=(12xx11xx10xx9xx(8!))/(8!)=11880.`
` "(ii) "^(75)P_(2)=(75!)/((75-4)!)=(75!)/(73!)=(75xx74xx(73)!)/(73!)=(75xx74)=5550.`
` "(iii) "^(8)P_(8)=8! =(8xx7xx6xx5xx4xx3xx2xx1)=40320.`
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RS AGGARWAL-PERMUTATIONS-SOLVED EXAMPLES
  1. Evaluate "(i) "^(12)P(4) " (ii) "^(75)P(2) " (iii) "...

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  2. Find the value of n such that "(i) "^(n)P(5) =42 xx ""^(n)P(3), n g...

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  3. Find r if (i) .^(5)P(r) = 2 .^(6)P(r-1) (ii) .^(5)P(r) =^(6)P(r-1).

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

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  5. (i) If ""^(15)P(r)=2730, find the value of r. (ii) If ""^(10)P(r)=5...

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  6. If .^56 P(r+6):^(54)P(r+3)=30800 :1, findr

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  7. If ^2n+1P(n-1):^(2n-1)Pn=3:5,fin dndot

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  8. If ""^(22)P(r+1):""^(20)P(r+2)=11:52, find r.

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  9. Prove that: (i) ""^(n)P(n)=""^(n)P(n-1) " (ii) "^(n)P(r)=n* ""^...

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  10. If r lt s le n " then prove that " ^(n)P(s) " is divisible by "^(n)P(r...

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  11. Find the number of permutations of 7 objects, taken 3 at a time.

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  12. Find the number of different permutations of the letters of the word ...

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  13. How many words can be formed using the letter A thrice, the letter B ...

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  14. (i) Find how many arrangements can be made with the letters of the wo...

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  15. Find the number of arrangements of the letters of the INDEPENDENCE....

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  16. How many different words can be formed by using all the letters of the...

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  17. In how many of the distinct permutations of the letters in MISSISSIPPI...

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  18. (i) How many words can be formed with the letters of the word, 'HARYAN...

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  19. In how many ways can the letters of the word 'PERMUTATIONS' be arrang...

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  20. If the different permutations of all the letter of the word EXAMINATIO...

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