Discussion

Question:

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

Explanation:

The following Venn diagram can be drawn from the given information.

Since students must choose at least 2 subjects, there will be no one who chose a single subject.

Now, maximum number of students who choose only Math and Physics can be 5. (∵ 23 students chose Math)

Hence, for Physics we still have 25 – 18 – 5 = 2 students left.

These 2 students will have to chose Chemistry along with Physics.

∴ Least number of students who can choose Chemistry = 2 + 18 = 20.

Hence, option (b).

» Your doubt will be displayed only after approval.

Doubts

shafi said (2022-11-16 13:37:54)

in 1st point why 5 student chooses math n physc they can also choose mth n chemstry then final answr will be dffrnt pls explain

Reply from Admin:

Since we have to minimise students who choose chemistry, we will have to maximise those students who will choose physics/maths.

18 students chose all three subjects. 23 students chose maths, hence maximum (23 - 18 =) 5 students can chose maths and physics only.

This leaves 2 (25 - 18 - 5) more students who have to chose physics. Since they cannot chose maths as 2nd subject, they will have to chose chemistry as 2nd subject.

Hence, minimum number of students choosing chemistry as their subject = 18 + 2 = 20.

Hope this helps !!!

Discussion

Doubts

Feedback