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

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

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

.^(n-1)C_(r)+^(n-1)C_(r-1)=

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

Prove that "^n C_r+^(n-1)C_r+...+^r C_r=^(n+1)C_(r+1) .

Prove that .^(n)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3) + "……" + (-1)^(r) .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ) .

Show that .^(n)C_(r)+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_(r) .

The result of ^(n-1)C_r+^(n-1)C_(r-1)=

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Show that , .^(n)C_(r)=(n-r+1)/(r).^(n)C_(r-1) .

The roots of the equation |^x C_r^(n-1)C_r^(n-1)C_(r-1)^(x+1)C_r^n C_r^n C_(r-1)^(x+2)C_r^(n+1)C_r^(n+1)C_(r-1)|=0 are a) x=n b) x=n+1 c) x=n-1 d) x=n-2

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

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  2. Find the exponent of 80 in 200!.

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

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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 ^ n P5=20 ^nP3 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. Simplify the following and express it in the form (a+ib): (3+4i)(2-3i...

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

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  15. If (n+3)! =56 x (n+1)!, Find the value of n.

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

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

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

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

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  20. Find the 28th term from the end term of the AP 6, 9, 12, 15, 18, ....,...

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