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Prove that ""^(10)C(3)+""^(10)C(6)=""^...

Prove that
`""^(10)C_(3)+""^(10)C_(6)=""^(11)C_(4)`

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The correct Answer is:
`("Since "^(n)C_(r)=""^(n)C_(n-r))=""^(11)C_(4)`
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Find the value of ""^(10)C_(5)+2. ""^(10)C_(4)+""^(10)C_(3) .

I : IF ""^(12)C_(r+1) ="" ^(12) C_(3r-5) then r=3 or 4 . II : If ""^(9) C_(3) +""^(9)C_(5) = ""^(10)C_(r) then r=4 or 6.

Prove that ""^(25)C_(4)+ Sigma_(r=0)^(4) ""^((29-r))C_(3)=""^(30)C_(4)

Show that ""^(10)C_2+^(11)C_2+^(12)C_2+^(13)C_2+...+^(20)C_2=^(21)C_3-^(10)C_3 .

Prove that : Prove that C_(0)+3.C_(1)+3_(2).C_(2)+……+3^(n).C_(n)=4^(n)

If ""^(9)C_(3)+""^(9)C_(5)=""^(10)C_(r) then find r.

Prove that 5.C_(0) +5^(2).(C_(1))/(2) +5^(3).(C_(2))/(3)+…+5^(n+1).(C_(n))/(n+1)=(6^(n+1)-1)/(n+1) Hence show that 5.C_(0) +(5^(2))/(2).C_(1)+(5^(3))/(3).C_(2)+….+(5^(11))/(11).C_(10)=(6^(11)-1)/(11)

Prove that 3.C_(0)^(2)+7.C_(1)^(2)+11.C_(2)^(2)+…..+(4n+3).C_(n)^(2)=(2n+3).""^(2n)C_(n).

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PERMUTATIONS AND COMBINATIONS-TAXTUAL EXERCISES
  1. Prove that ""^(10)C(3)+""^(10)C(6)=""^(11)C(4)

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  2. If ""^(n)P(7)=42. ""^(n)P(5). find n.

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  3. If ""^((n+1))P(5): ""^(n)P(6)=2:7, find

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  4. If ""^(12)P(5)+5. ""^(12)P(4)=""^(13)P(r), find r.

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  5. If ""^(18)P((r-1)):""^(17)P((r-1))=9:7, find r.

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  6. A man has 4 sons and there are 5 schools within his reach. In how many...

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  7. If there are 25 railway stations on a railway line, how many types of ...

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  8. In a class there are 30 students. On the New year day, every student p...

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  9. Find the number of ways of arranging the letters of the word TRIANGLE ...

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  10. Find the number of numbers that are greater than 4000 which can be for...

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  11. Find the number of ways of arranging the letters of the word MONDAY so...

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  12. Find the number of ways of arranging 5 different mathematics books, 4 ...

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  13. Find the number of 5 letter words that can be formed using the letters...

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  14. Find the number of ways of seating 10 students A(1), A(2)…..A(10) in a...

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  15. Find the number of ways in which 5 red balls, 4 black balls of differe...

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  16. Find the number of ways in which 5 red balls, 4 black balls of differe...

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  17. Find the number of 4 - digit numbers that can be formed using the digi...

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  18. If the letters of the word BRING are permuted in all possible ways and...

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  19. Find the sum of all 4 digited numbers that can be formed using the dig...

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  20. There are 9 objects and 9 boxes. Out of 9 objects, 5 cannot fit in thr...

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  21. Find the number of 4- digited numbers that can be formed using the dig...

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