Question

A classroom of 20 students can be categorized on the basis of blood-types: 5 students each with a, b, ab, and o blood-types. If four students are selected at random from this class, what is the probability that each student has a different blood-type?

Answer 1

Answer:  The answer is 5.63%.

Step-by-step explanation: Given that a classroom has 20 students, that can be categorized on the basis of blood types. Each of a group of 5 students have a blood group a, b, ab and o.

Therefore, the probability that the 4 students selected at random has a different blood type is given by

$p\\\\=\dfrac{\frac{4!}{1!3!}\times \frac{4!}{1!3!}\times \frac{4!}{1!3!}\times \frac{4!}{1!3!}}{\frac{20!}{4!16!}}\\\\\\=\dfrac{4\times 4\times 4\times 4}{5 \times 19\times 3\times 17}\\\\\\=\dfrac{256}{4845}=5.63\%.$

Thus, the required probability is 5.63%.