Chapter 12.4, Problem 1CYP

To determine

To find : Probability of $2$ juniors and $2$ seniors are selected.

Answer to Problem 1CYP

  $\frac{\text{15}}{\text{91}}$

Explanation of Solution

Given information :

Three juniors and eleven seniors nominated for $4$ spots to represent the school.

Formula Used:

Probability P(E) = $\frac{\text{No}\text{. of favourable outcomes}}{\text{Total possible outcomes}}$

Calculation:

Total possible outcomes = ${}^{\text{14}}{C}_4$

No. of favourable outcomes = ${}^{\text{3}}{C}_2\times {}^{11}{C}_2$

So, required probability = $\frac{{}^{\text{3}}{C}_2\times {}^{11}{C}_2}{{}^{11}{C}_4}$

As ${}^n{c}_r=\frac{n!}{r!(n-r)!}$

Required probability = $\frac{\text{3}\times \text{55}}{\text{7}\times \text{13}\times \text{11}}$

  $=\frac{15}{91}$