In the club election, the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be 62, then the number of candidates is: (a) 7 (b) 5 (c) 6 (d) 8

Options

A. 7
B. 5
C. 6
D. 8

Answer

To solve the problem step by step, let's denote the number of candidates as \( n \). According to the problem, the number of contestants is one more than the number of maximum candidates for which a voter can vote. Therefore, we can say:

1. **Define the variables**:
Let \( n \) be the number of candidates. The maximum number of candidates a voter can vote for is \( n - 1 \).

2. **Calculate the total voting possibilities**:
The total number of ways a voter can vote is given by the formula:
\[ \text{Total ways} = 2^n - 2 \]
Here, \( 2^n \) accounts for all possible combinations of voting (including not voting for anyone and voting for everyone), and we subtract 2 to exclude the cases where a voter votes for no one and where a voter votes for everyone.

3. **Set up the equation**:
According to the problem, the total number of ways a voter can vote is 62. Therefore, we can set up the equation:
\[ 2^n - 2 = 62 \]

4. **Solve for \( n \)**:
Rearranging the equation gives:
\[ 2^n = 62 + 2 \]
\[ 2^n = 64 \]
Now, we can express 64 as a power of 2:
\[ 64 = 2^6 \]
Thus, we have:
\[ n = 6 \]

5. **Conclusion**:
The number of candidates is \( n = 6 \).

### Final Answer:
The number of candidates is **6** (option c).