Home
Class 11
MATHS
If N denotes the number of ways of s...

If `N` denotes the number of ways of selecting `r` objects of out of `n` distinct objects `(rgeqn)` with unlimited repetition but with each object included at least once in selection, then `N` is equal is a. `.^(r-1)C_(r-n)` b. `.^(r-1)C_n` c. `.^(r-1)C_(n-1)` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CENGAGE ENGLISH|Exercise All Questions|173 Videos
  • PROBABILITY

    CENGAGE ENGLISH|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

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

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

The value of sum_(r=0)^(n-1)^n C_r//(^n C_r+^n C_(r+1)) equals a. n+1 b. n//2 c. n+2 d. none of these

If .^(n)C_(r-1)=36, .^(n)C_(r)=84 and .^(n)C_(r+1)=126 , find n and r.

If .^(n-1)C_r:^nC_r:^(n+1)C_r=6:9:13 find n and r.

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

If .^(n)C_(r-1): .^(n)C_(r): .^(n)C_(r+1)=3:4:5 , find the values of n and r.

n points are given of which r points are collinear, then the number of straight lines that can be found = (a) ""^(n)C_(2)-""^(r)C_(2) (b) ""^(n)C_(2)-""^(r)C_(2)+1 (c) ""^(n)C_(2)-""^(r)C_(2)-1 (d) None of these

CENGAGE ENGLISH-PERMUTATIONS AND COMBINATIONS-All Questions
  1. Rajdhani Express going from Bombay to Delhi stops at five intermedi...

    Text Solution

    |

  2. In a certain test, there are n question. In the test, 2^(n-i) studen...

    Text Solution

    |

  3. If N denotes the number of ways of selecting r objects of out ...

    Text Solution

    |

  4. Number of ways in which 30 identical things are distributed among six ...

    Text Solution

    |

  5. If 10! =2^p .3^q .5^r .7^s, then (A) 2q = p (B) pqrs = 64 (C) number...

    Text Solution

    |

  6. A is a set containing n elements. A subset P1 is chosen and A is recon...

    Text Solution

    |

  7. Let n be a four-digit integer in which all the digits are different....

    Text Solution

    |

  8. If P = 21(21^2-1^2)(21^2-2^2)(21^2-3^2)...............(21^2-10^2),t h ...

    Text Solution

    |

  9. Statement 1: number of ways in which 10 identical toys can be distri...

    Text Solution

    |

  10. Statement 1: The number of positive integral solutions of a b c=30 is...

    Text Solution

    |

  11. Prove by combinatorial argument that .^(n+1)Cr=^n Cr+^n C(r-1)dot

    Text Solution

    |

  12. Prove that (n !)! is divisible by (n !)^((n-1)!)

    Text Solution

    |

  13. Column I, Column II Number of straight lines joining any two of ...

    Text Solution

    |

  14. If the number of selections of 6 different letters that can be made...

    Text Solution

    |

  15. If n1 and n2 are five-digit numbers, find the total number of ways...

    Text Solution

    |

  16. If n1a n dn2 are five-digit numbers, find the total number of ways ...

    Text Solution

    |

  17. If a denotes the number of permutations of (x+2) things taken all at a...

    Text Solution

    |

  18. If n Pr=^n P(r+1) and n Cr=^n C(r-1,) then the value of (n+r) i...

    Text Solution

    |

  19. Let n be the number of ways in which 5 boys and 5 girls can stand in a...

    Text Solution

    |

  20. (i) In how many ways can a pack of 52 cards be divided equally amon...

    Text Solution

    |