Question

The number of selecting at least $4$ candidates from $8$ candidates is

• A. $270$
• B. $70$
• C. $163$
• D. None of these

Answer 1

The correct option is C

$163$

Explanation for correct option

Given, there are total $8$ candidate from which we need to select at least $4$ candidate.

Therefore, total number of ways

1. Selecting exactly $4$ candidate out of $8$ candidate$={{}^{8}C}_4=70$
2. Selecting exactly $5$ candidate out of $8$ candidate$={{}^{8}C}_5=56$
3. Selecting exactly $6$ candidate out of $8$ candidate$={{}^{8}C}_6=28$
4. Selecting exactly $7$ candidate out of $8$ candidate$={{}^{8}C}_7=8$
5. Selecting exactly $8$ candidate out of $8$ candidate$={{}^{8}C}_8=1$

Total number of ways$=70+56+28+8+1=163$

Hence, the correct option is $\left(\mathrm{C}\right)$