Chapter 12.4, Problem 1CYU

To determine

To find:- The Probability that $3$ of the $8$ Paul Gauguin painting selected.

Answer to Problem 1CYU

  $\text{0}\text{.138}$

Explanation of Solution

Given information :

Total paintings are $20$ and $4$ to be selected.

Formula Used:

  ${}^n{C}_r=\frac{n!}{r!(n-r)!}$

Calculation:

Total No. of favourable outcomes = ${}^{\text{8}}{C}_3\times {}^{12}{C}_1$

Total Possible outcomes = ${}^{\text{20}}{C}_4$

Required probability = $\frac{{}^8{C}_3\times {}^{12}{C}_1}{{}^{20}{C}_4}$

  $=\frac{56\times 12}{4845}=\frac{672}{4845}=\frac{224}{1615}=0.138$