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Prove that : "^nPn= 2^nP(n-2)....

Prove that :
`"^nP_n= 2^nP_(n-2)`.

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Find n if : 2^5P3= "^nP4.

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  2. Find n if "^(n-1)P3 : "^nP4 =1:9.

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  3. Prove that : "^nPn= 2^nP(n-2).

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  4. Prove that : ^10P3= "^9P3+3^9P2.

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  5. Show that ^nPn= "^nP(n-1) for all natural numbers n .

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  6. How many 3-digit numbers can be formed by using the digits 1 to 9 if n...

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  7. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4,...

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  8. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4...

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  9. In how many ways can five children stand in a queue ?

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  10. How many different signals can be generated from 6 flags of different ...

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  11. Seven songs are to be rendered in a programme. In how many different o...

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  12. There are 6 items in column A and 6 items in column B. A student is as...

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  13. How many 3-digit numbers are there without repetition?

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  14. How many 4-digit numbers are there with no digit repeated?

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  15. How many natural numbers from 1 to 1000 have none of their digits repe...

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  16. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4,...

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  17. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4...

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  18. Find the number of 4-digit numbersthat can be formed using the digits ...

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

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  20. How many 4 digits numbers can be formed from the digits 1 to 9 if not ...

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