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

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

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

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

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

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

Prove that , .^(n)C_(r)+3.^(n)C_(r-1)+3.^(n)C_(r-2)+^(n)C_(r-3)=^(n+3)C_(r)

.^(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

If n is a positive integer then using the indentiy (1+x)^(n)=(1+x)^(3)(1+x)^(n-3) , prove that ""^(n)C_(r)=""^(n-2)C_(r)+3*""^(n-3)C_(r-1)*""^(n-3)C_(r-2)+""^(n-3)C_(r-3)

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

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. If m=.^(n)C(2) show that , .^(m)C(2)=3.^(n+1)C(4)

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  2. Find n and r if .^(n)P(r)=.^(n)P(r+1)and^(n)C(r)=^(n)C(r-1).

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

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

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  5. .^(n)C(r)+2.^(n)C(r-1)+.^(n)C(r-2)=.^(n+2)C(r)(2lerlen).

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  6. Show that , (.^(n)C(r)+^(n)C(r-1))/(.^(n)C(r-1)+^(n)C(r-2))=(.^(n+1)p...

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  7. Prove that , .^(45)C(8)+sum(r=1)^(7).^(52-r)C(7)+sum(k=1)^(5).^(57-K)C...

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  8. Prove that , .^(15)C(8)+^(15)C(9)-.^(15)C(6)-^(15)C(7)=0

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  9. Prove that , .^(n)C(r)+3.^(n)C(r-1)+3.^(n)C(r-2)+^(n)C(r-3)=^(n+3)C(r)

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  10. Show that (.^(4n)C(2n))/(.^(2n)C(n))=(1.3.5......(4n-1))/({1.3.5........

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  11. If .^(n)C(r-1)=36,.^(n)C(r)=84and.^(n)C(r+1)=126 find n and r .

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  12. If (.^(n)C(r-1))/(a)=(.^(n)C(r))/(b)=(.^(n)C(r+1))/(c) n=(ab+2ac...

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  13. If the number of permutations of n different things taken r at time be...

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  14. For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

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  15. Evaluate : .^(20)C(5)+sum(j=2)^(5).^(25-j)C(4)

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  16. If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .

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  17. Solve : ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=(3)/(5),( x in N N)

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  18. Prove that if ngt7 then .^(n-1)C(3)+.^(n-1)C(4)gt^(n)C(3)

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  19. How many different triangles can be formed by joining the angular poi...

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  20. How many words each consisting of five different letters can be formed...

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