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

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

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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 ) .

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

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

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

If .^(n)C_(4)=.^(n)C_(2) , then find .^(n)C_(3) .

If .^(n)C_(3)=k.n(n-1)(n-2) then k=

If .^(n)C_(5)=.^(n)C_(4) , then find .^(n)C_(7) .

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

Solve the inequality .^(n-1)C_4 - .^(n -1)C_3 - 5/4 .^(n-2)C_2 lt 0,n in N

CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .

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

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

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

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

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  6. find the number of different words that can be formed from 12 consonan...

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  7. A person has got 15 acquaintances of whom 10 are relatives . In how ma...

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  8. In how many different ways can 9 men be selected from 15 men so as to ...

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  9. In how many ways can a committee of a 3 ladies and 4 gentlemen be appo...

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  10. m men and n women are to be seated in a row that no two women sit tog...

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  11. Eight prizes are to be distributed by a lottery . The first participa...

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  12. In an election there are 7 candidates and 4 members are to be elected...

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  13. In a plane there are 10 points out of which no three are collinear exc...

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  14. If 20 straight lines be drawn in a plane , no two of them being parall...

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  15. If 10 parallel lines in a plane are intersected by a family of anothe...

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  16. There are 15 points in a plane of which 4 points lie in one stright li...

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  17. Show that in the number of combinations of 2n different things taken n...

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  18. How many different numbers of 6 digits each (without repetition of dig...

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  19. If the number of combinations of n different things taken (r+r) at a t...

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  20. In how many ways can a person contribute to a charitabe fund out of 10...

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