MHTCET 13 May 2023 Shift 2 Solved Paper

Here, 5 students are to be selected from n students.
When 2 specified students are included, then remaining 3 students can be selected (n−2) students
∴ Number of ways of selecting 3 student from n students =‌(n−2)C3
Now, when 2 specified students are not included, then 5 students can be selected from the remaining (n−2) students.
∴ Number of ways of selecting 5 students from (n−2) students =‌n−2C5
According to question,
‌‌n−2C3:‌n−2C5=2:3
⇒‌‌‌

(n−2)!

3!(n−5)!

×‌

5!(n−7)!

(n−2)!

=2:3
⇒‌

5!

3!

‌

(n−7)!!

(n−5)!

=‌

2

3

⇒‌

5×4

(n−5)(n−6)

=‌

2

3

∴ Then, value of n=11