The number of ways of selecting atleast 4 candidates from 8 candidates is:

Options

A. 270
B. 70
C. 163
D. none

Answer

To find the number of ways of selecting at least 4 candidates from 8 candidates, we can break the problem down into several steps.

### Step-by-step Solution:

1. **Understanding the Problem**: We need to select at least 4 candidates from a total of 8 candidates. This means we can select 4, 5, 6, 7, or all 8 candidates.

2. **Using Combinations**: The number of ways to select \( r \) candidates from \( n \) candidates is given by the combination formula \( \binom{n}{r} \). In our case, we will calculate:
- \( \binom{8}{4} \) for selecting 4 candidates
- \( \binom{8}{5} \) for selecting 5 candidates
- \( \binom{8}{6} \) for selecting 6 candidates
- \( \binom{8}{7} \) for selecting 7 candidates
- \( \binom{8}{8} \) for selecting all 8 candidates

3. **Calculating Each Combination**:
- \( \binom{8}{4} = \frac{8!}{4!(8-4)!} = \frac{8!}{4!4!} = 70 \)
- \( \binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!} = 56 \)
- \( \binom{8}{6} = \frac{8!}{6!(8-6)!} = \frac{8!}{6!2!} = 28 \)
- \( \binom{8}{7} = \frac{8!}{7!(8-7)!} = \frac{8!}{7!1!} = 8 \)
- \( \binom{8}{8} = \frac{8!}{8!(8-8)!} = \frac{8!}{8!0!} = 1 \)

4. **Summing the Combinations**: Now, we will add all these values together to find the total number of ways to select at least 4 candidates:
\[ \text{Total} = \binom{8}{4} + \binom{8}{5} + \binom{8}{6} + \binom{8}{7} + \binom{8}{8} = 70 + 56 + 28 + 8 + 1 = 163 \]

5. **Final Answer**: Therefore, the number of ways of selecting at least 4 candidates from 8 candidates is \( 163 \).