At an election a voter may vote for nany number of candidates , not greater than the number t be eected. There are 10 candidates and 4 are to be elected. If a voter for at lest one candidates, thene the number of ways in which he can vote is (A) 5040 (B) 6210 (C) 385 (D) 1110

Options

A. 5040
B. 6210
C. 385
D. 1110

Explanation

To solve the problem of how many ways a voter can vote for at least one candidate out of 10 candidates when 4 candidates are to be elected, we can follow these steps:

### Step 1: Determine the total number of ways to choose candidates
The voter can choose from 1 to 4 candidates from the 10 available candidates. We can calculate the number of ways to choose k candidates from n candidates using the combination formula:

\[ C(n, k) = \frac{n!}{k!(n-k)!} \]

### Step 2: Calculate the combinations for each possible choice
1. **Choosing 1 candidate**:
\[ C(10, 1) = \frac{10!}{1!(10-1)!} = 10 \]

2. **Choosing 2 candidates**:
\[ C(10, 2) = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45 \]

3. **Choosing 3 candidates**:
\[ C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 \]

4. **Choosing 4 candidates**:
\[ C(10, 4) = \frac{10!}{4!(10-4)!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210 \]

### Step 3: Sum the combinations
Now, we add the number of ways to choose 1, 2, 3, and 4 candidates:

\[ C(10, 1) + C(10, 2) + C(10, 3) + C(10, 4) = 10 + 45 + 120 + 210 = 385 \]

### Step 4: Conclusion
Thus, the total number of ways in which a voter can vote for at least one candidate is **385**.

### Final Answer
The answer is (C) 385.