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Compute the""^7C3+""^6C4+""6C3...

Compute the`""^7C_3+""^6C_4+""6C_3`

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`""^7C_3+""^6C_4+""^6C_3=""^7C_3+""^6C_4+""^6C_(4-1)`
` =""^7C_3+""^(6+1)C_4 = ""^7C_3+""^7C_4`
`( :'""^nC_r+""^nC_(r-1)=""^(n+1)C_r)`
` = ""^7C_4+""^7C_(4-1)=""^(7+1)C_4`
`= ""^8C_4=(8!)/(4!(8-4)!)=(8*7*6*5)/(4*3*2*1)=70`
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MBD PUBLICATION-PERMUTATIONS AND COMBINATIONS-QUESTION BANK
  1. Compute the ^15C12

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  2. Compute the ""^9C4 + ""^9C5

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  3. Compute the""^7C3+""^6C4+""6C3

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  4. Compute the""^8C0+""^8C1+……+""^8C8

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  5. Solve ""^nC4=""^nC11,

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  6. Solve ""^(2n)C3:""^nC3=44:5

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  7. Find n and r if ""^nPr=1680,""^nCr=70.

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  8. How many diagonals can an n-gon (a polygon with n sides ) have ?

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  9. If a set A has n elements and another set B has m elements, what is th...

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  10. From five consonants and four vowels, how many words consist of three ...

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  11. In how many ways can a committee of four gentlemen and three ladies b...

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  13. How many triangles can be drawn by joining the vertices of a decagon ?

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  14. How many triangles can be drawn by joining the vertices and the centre...

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  15. Sixty points lie on a plane, out of which no three points are collinea...

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  16. In how many ways can 10 boys and 10 girls sit in a row so that no two ...

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  17. In how many ways can six men and seven girls sit in a row so that the ...

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  18. How many factors does 1155 have that are divisible by 3?

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  19. How many factors does 210 have ?

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  20. If n is a product of k distinct primes what is the total number of fac...

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