ISI-2017-6

Question

In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible number of boys without glasses is

• A. $\{0,.....,30\}$
• B. $\{10,....,30\}$
• C. $\{0,.....,40\}$
• D. $\text{none of these}$

Comments

is it A?

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Good approach:

https://www.wyzant.com/resources/answers/478525/probability

Answer 1

Among $80$ students $50$ students wear glasses.

Now, we have to find out set of all possible numbers without glasses 

No. of students wear glasses-

1. When Girls = $10$, Boys = $40 \text{ Remaining Boys without glasses=}0 \rightarrow \text{ possible}$
2. When Girls = $20$, Boys = $30 \text{ Remaining Boys without glasses=}10 \rightarrow \text{ possible}$
3. When Girls = $25$, Boys = $25 \text{ Remaining Boys without glasses=}15\rightarrow \text{ possible}$
4. When Girls = $30$, Boys = $20 \text{ Remaining Boys without glasses=}20 \rightarrow \text{ possible}$
5. When Girls = $40$, Boys = $10 \text{ Remaining Boys without glasses=}30 \rightarrow \text{ possible}$
6. If  Boys = $0$, then Girls = $50  \rightarrow \text{ not possible as Total girls is 40}$

$∴\color{green}{\text{ Answer will be}} \color{Purple}{\text{ option A) }} \color{pink}{ \{0,....30\}}$

Comments

Yes ankit, they're represented in $\color{red}{Set}$

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@ankitgupta

NULL set means there are 0 elements

right?

that exactly represented here

right?

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yeah

Answer 2

{0,,,,,,30} ->(A)