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Show that ^nPn= "^nP(n-1) for all natura...

Show that `^nP_n= "^nP_(n-1)` for all natural numbers n .

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Prove that : ^nP_r= n"^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

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

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

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Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Prove that : "^nPn= 2^nP(n-2).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 a...

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