Home
Class 12
MATHS
If n denotes the number of ways of se...

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

A

`.^(r-1)C_(r-n)`

B

`.^(r-1)C_(n)`

C

`.^(r-1)C_(n-1)`

D

`.^(r-1)C_(r-n-1)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`becausex_(1)+x_(2)+x_(3)+ . . .+x_(n)=r, Aa x_(i)ge1,(1 le I le )`
Total number of such solutions `=.^(r-1)C_(n-1)=.^(r-1)C_(r-n)`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|15 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

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

prove that total number of ways of selection of r points out of n points in a row such that no two of them are consecutive C(n-r+1,r)

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

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

What is C(n, r) + 2C(n, r - 1) + C(n, r - 2) equal to?

If C_r stands for ^nC_r and sum_(r=1)^n (r.C_r)/(C_(r-1)=210 then n= (A) 19 (B) 20 (C) 21 (D) none of these

If 1<=r<=n, then n^(n-1)C_(r)=(n-r+1)^(n)C_(r-1)