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Prove that .^(n-1) Pr+r .^(n-1) P(r-1) =...

Prove that `.^(n-1) P_r+r .^(n-1) P_(r-1) = .^nP_r`

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CENGAGE ENGLISH-PERMUTATIONS AND COMBINATIONS-All Questions
  1. Find the sum of the series sum(r=1)^n rxxr !dot

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  2. Find the exponent of 80 in 200!.

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  3. Prove that .^(n-1) Pr+r .^(n-1) P(r-1) = .^nPr

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  4. How many ways are there to seat n married couples (ngeq3) around a tab...

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  5. A round-table conference is to be held among 20 delegates belonging fr...

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  6. How many numbers can be formed from the digits 1, 2, 3, 4 when repetit...

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  7. Find the three-digit odd numbers that can be formed by using the digit...

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  8. If nP5=20nP3 find the value of n

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  9. Find the total number of ways of selecting five letters from the word ...

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  10. Passengers are to travel by a double decked bus which can accommodate ...

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  11. A delegation of four students is to be selected from al total of 12 ...

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  12. In a conference 10 speakers are present. If S1 wants to speak before S...

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  13. Five boys and five girls sit alternately around a round table. In how ...

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  14. Find the number of ways in which A A A B B B can be places in the squa...

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  15. A regular polygon of 10 sides is constructed. In how many way can 3...

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  16. In ;a plane, there are 5 straight lines which will pass through a give...

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  17. If ^15 C(3r):^(15)C(r+1)=11 :3 , find the value of rdot

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  18. If the ratio ^2n C3:^n C3 is equal to 11:1 find ndot

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  19. There are n married couples at a party. Each person shakes hand with e...

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  20. Twenty-eight games were played in a football tournament with each team...

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