Question

There are k baskets and n balls. The balls are put into the baskets randomly. If

k<n,

1. There is no empty basket

2. There are exactly (n- k) baskets with at least one ball

3. There is at least one basket with two or more balls

4. There are (n- k) baskets with exactly two bal​

Answer 1

Answer:

[c] There is at least one basket with two or more balls.

Step-by-step explanation:

-> This question is based on the pigeonhole principle.

-> The pigeonhole principle states that "If n items are put into m containers, with n > m, then at least one container must contain more than one item".

-> Let us consider n = 3 and k = 2. There are two ways to fill 2 baskets with 3 balls.

1. We may fill a basket with 2 balls and another with one ball.

2. We may fill a basket with 3 balls and leave another one empty.

-> Based on the principle, option a is wrong because there is a possibility of putting all the balls in a single basket, so that another basket will be empty.

-> Option b is wrong as we can't assure that there are exactly (n - k) baskets with at least one ball.

-> Option c is right for both cases.

-> Option d is wrong because we can't assure that there are (n - k) baskets with exactly two balls.