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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)`
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