Home
Class 11
MATHS
If ""^(m)C(r)=0" for "rgtm then the sum ...

If `""^(m)C_(r)=0" for "rgtm` then the sum `sum_(r=0)^(m)""^(18)C_(r)""^(20)C_(m-r)` is maximum when m =

A

20

B

19

C

10

D

10

Text Solution

Verified by Experts

We have,
`sum_(r=0)^(m)""(18)C_(r)""^(20)xxC_(m-r)`
= Number of ways of choosing m persons out of 18 men and 20 women
`=""^(38)C_(m)`
Clearly, it is maximum when m =19.
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|9 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|136 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

Similar Questions

Explore conceptually related problems

The sum sum_(r=0)^(m) ""^(10)C_(r) xx""^(20)C_(m -r) is maximum . When m=

Find the sum sum_(r=0)^(5)""^(32)C_(6r) .

Find the sum sum_(r=0)^n^(n+r)C_r .

Find the sum sum_(r=0)^n^(n+r)C_r .

sum_(r=0)^(n)(""^(n)C_(r))/(r+2) is equal to :

Find the sum_(r =0)^(r) ""^(n_(1))C_((r-i))""^(n_(2))C_(i) .

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

sum_(r=0)^(4) (-1)^(r )""^(16)C_(r) is divisible by :

The sum of the series sum_(r=0) ^(n) "r."^(2n)C_(r), is

OBJECTIVE RD SHARMA ENGLISH-PERMUTATIONS AND COMBINATIONS-Section I - Solved Mcqs
  1. The total numbre of intergral solutins of abc =24, is

    Text Solution

    |

  2. A bag contains 3 black, 4 white and 2 red balls, all the balls being d...

    Text Solution

    |

  3. The number of different pairs of words (,) that can be made with the l...

    Text Solution

    |

  4. In the decimal system of numeration the number of 6-digit numbers in w...

    Text Solution

    |

  5. There are 60 questions in a question paper. If no two students solve t...

    Text Solution

    |

  6. An n-digit number is a positive number with exactly n digits. Ni...

    Text Solution

    |

  7. How many ways are there to arrange the letters in the word GARDEN with...

    Text Solution

    |

  8. The number of ways of distributing 8 identical balls in 3 distinct box...

    Text Solution

    |

  9. The number of seven-digit numbers, with sum of the digits equal to 10 ...

    Text Solution

    |

  10. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  11. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  12. Consider all possible permutations of the letters of the word ENDEANOE...

    Text Solution

    |

  13. All possible permutations of the letters of the word ENDEANOEL if A, E...

    Text Solution

    |

  14. If ""^(m)C(r)=0" for "rgtm then the sum sum(r=0)^(m)""^(18)C(r)""^(20)...

    Text Solution

    |

  15. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  16. There are two urns. Urn A has 3 distinct red balls and urn B has 9 dis...

    Text Solution

    |

  17. There are 10 points in a plane , out of these 6 are collinear .if N is...

    Text Solution

    |

  18. The total number of ways in which 5 balls of different colours can be ...

    Text Solution

    |

  19. There are 10 girls and 8 boys in a class room including Mr. Ravi, Ms. ...

    Text Solution

    |

  20. The number of words which can be formed out of the letters a, b, c, d,...

    Text Solution

    |