At an election there are five candidates and three members to be elected, and an elector may vote for any number of candidates not greatre than the number to be elected. Then the number of ways in which an elector may vote, is

Options

A. 25
B. 30
C. 32
D. none of these

Answer

To solve the problem step by step, we will calculate the number of ways an elector can vote for the candidates.

### Step 1: Understand the voting options
An elector can vote for:
- 1 candidate
- 2 candidates
- 3 candidates

### Step 2: Calculate the number of ways to vote for 1 candidate
The number of ways to choose 1 candidate from 5 candidates is given by the combination formula \( \binom{n}{r} \), where \( n \) is the total number of candidates and \( r \) is the number of candidates to choose.

\[ \text{Ways to choose 1 candidate} = \binom{5}{1} = 5 \]

### Step 3: Calculate the number of ways to vote for 2 candidates
The number of ways to choose 2 candidates from 5 candidates is:

\[ \text{Ways to choose 2 candidates} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]

### Step 4: Calculate the number of ways to vote for 3 candidates
The number of ways to choose 3 candidates from 5 candidates is:

\[ \text{Ways to choose 3 candidates} = \binom{5}{3} = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10 \]

### Step 5: Sum the total number of ways to vote
Now, we add the number of ways for each voting option:

\[ \text{Total ways to vote} = \binom{5}{1} + \binom{5}{2} + \binom{5}{3} = 5 + 10 + 10 = 25 \]

### Final Answer
Thus, the total number of ways in which an elector may vote is **25**.

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