Home
Class 12
MATHS
If ""^(n)C(r) denotes the number of comb...

If `""^(n)C_(r)` denotes the number of combinations of n things taken r at a time, then the expression `""^(n)C_(r+1)+""^(n)C_(r-1)+2xx""^(n)C_(r)`, equals

A

`""^(n+2)C_(r+1)`

B

`""^(n+1)C_(r)`

C

`""^(n+1)C_(r+1)`

D

`""^(n+2)C_(r)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|65 Videos

  • MATHEMATICAL REASONING

    NEW JOYTHI PUBLICATION|Exercise QUESTION FROM COMPETITIVE EXAMS|23 Videos

  • PRINCIPLES OF MATHEMATICAL INDUCTION

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|4 Videos

Similar Questions

Explore conceptually related problems

Prove that ""^(n)C_r + ""^(n)C_(r-1) = ""^(n+1)C_r

Prove ""^(n)P_(r)=""^(n-1)P_(r) +r. ""^(n-1)P_(r-1)

If ""^(n)P_(r)=720" "^(n)C_(r) , then r is equal to

.^((n-1)C_(r) + ^((n-1)) C_((r-1)) is

If n and r are two positive integers such that nger,"then "^(n)C_(r-1)+""^(n)C_(r)=

""".^(n-1)C_r + """.^(n-1)C_(r-1) is …………. .

Prove that if 1 le r le n " then " n xx^((n-1))C_(r-1)= (n-r+1).^(n)C_(r-1)

Verify the property ""^(n)C_(r)=n/r ""^(n-1)C_(r-1) where n=6 and r=3.

If ""^(nP_(r)=""^(n)P_(r+1) and ""^(n)C_(r)=""^(n)C_(r-1) find n and r.

NEW JOYTHI PUBLICATION-PERMUTATIONS AND COMBINATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. There are 10 persons including 3 ladies. A committee of 4 persons incl...

    Text Solution

    |

  2. If ""^(n)C(3)=10, then n is

    Text Solution

    |

  3. How many numbers with no more than three digits can be formed using on...

    Text Solution

    |

  4. If 8![1/(3!)+5/(4!)]=""^(9)P(r), then the value of r is equal to

    Text Solution

    |

  5. The sides BC, CA, AB of a triangle ABC have 3, 4 and 5 interior points...

    Text Solution

    |

  6. How many four digit numbers abcd exist such that a is odd, b is divisi...

    Text Solution

    |

  7. How many numbers lying between 100 and 1000 can be formed with the di...

    Text Solution

    |

  8. Total number of four digit odd numbers that can be formed using 0, 1, ...

    Text Solution

    |

  9. The number of ways in which 6 men and 5 women can dine at a round tabl...

    Text Solution

    |

  10. A student is to answer 10 out of 13 questions in an examination such t...

    Text Solution

    |

  11. If ""^(n)C(r) denotes the number of combinations of n things taken r a...

    Text Solution

    |

  12. How many ways are there to arrange the letters of the word "Garden" w...

    Text Solution

    |

  13. Then number of ways of distributing 8 identical balls in 3 distinct bo...

    Text Solution

    |

  14. The range of the function f(x)=""^(7-x)P(x-3) is

    Text Solution

    |

  15. If the letters of the word SACHIN are arranged in all possible ways an...

    Text Solution

    |

  16. The value of ""^(50)C(4)+sum(r=1)^(6)""^(56-r)C(3) is

    Text Solution

    |

  17. At an election, a voter may vote for any number of candidates, not gre...

    Text Solution

    |

  18. In a shop there are five types of ice - creams available. A child buys...

    Text Solution

    |

  19. How many different words can be formed by jumbling the letters in the ...

    Text Solution

    |

  20. The set S={1,2,3,....,12} is to be partitioned into three sets A, B, C...

    Text Solution

    |