Question

Three different prizes have to be distributed among 4 different students. Each student could get 0 to 3 prizes. If all the prizes were distributed, find the probaility that exactly 2 students did not receive a prize

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

Probability is an area of mathematics that deals with numerical descriptions of the likelihood of an event occurring or a statement being true. A value between 0 and 1 represents an event's probability.

Given:

There are three different prizes.

The total number of students are $4$.

Find:

The probability that $2$ students did not receive prizes.

Solution:

The total number of ways to distribute $3$ prizes among $4$ students is $4^3$.

The number of ways where$2$  students did not receive the prize is

$=$ the number of ways to distribute $3$ prizes among $2$ students.

$=2^3$

The probability of not getting prizes to exactly $2$ students $=\frac{2^3}{4^3}$

Hence, the probability of not getting prizes to exactly $2$ students is $\frac{1}{8}$