First slide

Combinations

Question

On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are

Moderate

A

42
B

34
C

25
D

None of these

Solution

Let n be the number of students.
Now, number of ways in which two students can be selected out of n students is $^{n} C_{2}$ .
∴ number of pairs of students $=^{n} C_{2}$ .
But for each pair of students, number of cards sent is 2 (since if there are two students A and B, A will send a card to B and B will send a card to A).
∴ For $^{n} C_{2}$ pairs, number of cards sent $= 2 \cdot^{n} C_{2}$ .
According to the question, $2 \cdot^{n} C_{2} = 600$
or, $2 \cdot \frac{n (n - 1)}{2!} = 600$
or, n² – n – 600 = 0
or, (n – 25) (n + 24) = 0
∴ n = 25, –24
But n ≠ –24
∴ n = 25.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App