1.

What is the total number of combination of n different things taken 1, 2, 3,...,n at a time ?A. `2^(n +1)`B. `2^(2n + 1)`C. `2^(n -1)`D. `2^(n -1)`

Answer» Correct Answer - D
Since, combinations of taking 1, 2, 3, ..., n things at a times are `.^(n)C_(1), .^(n)C_(2), ...., .^(n)C_(n)`
`:.` Total number of combinations
`= .^(n)C_(1) + .^(n)C_(2) + ....+ .^(n)C_(n)`
`= 1 + .^(n)C_(1) + .^(n)C_(2) +....+ .^(n)C_(n) - 1`
`= 2^(n) -1`


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