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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
- Prove that 1 + ^3C1+ ^4C2= ^5C3.
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- Determine n if "^(2n)C3 : "^nC3 = 11 : 1
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- If "^(2n)C3 : ^nC2= 12: 1, find n .
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- If .^(n)C(r )r: ^(n)C(r+1)=1:2 and .^(n)C(r+1): ^(n)C(r+2)=2:3, find ...
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- If "^(n-1)Cr : ^nCr : ^(n+1)Cr= 6:9: 13, find n and r.
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- If m= "^nC2, prove that "^m C2 =3xx ^(n+1)C4.
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- Prove that "^nCr+2 ^(n)C(r-1)+ ^(n)C(r-2) = ^(n+2)Cr.
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- Prove that "^nPr= ^nCr ^rPr.
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- Prove that "^nCr ^rC5= ^nC5 ^(n-5)C(r-5).
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- Prove that the product of any k consecutive integers is divisible by k...
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- Show that ((n+1)(n+2)(n+3)...... (n+r))/(r!) is a whole number.
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- Prove that "^(n-1)C3+ ^(n-1)C4 > ^nC3 if n >7.
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- Verify that ""^nCr= frac (n)(r) "^(n-1)C(r-1) and hence prove that "^n...
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- Find n if ""^nC4 , ""^nC5 and ""^nC6 are in A.P.
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- In how many ways can 5 sportsmen be selected from a group of 10 ?
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- How many selections of 4 books can be made from 8 different-books ?
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- A committee of 2 boys is to be selected from 4 boys. In how many ways ...
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- In how many ways can a committee be selected from 15 persons if the co...
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- In how many ways can a committee be selected from 15 persons if the co...
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- Sudha wants to choose any 9 stamps from a set of 11 different stamps. ...
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