Chapter 12.6, Problem 39STP

To determine

To find : Probability that $4$ posters will be for comedy movies and $4$ will be for family movies.

Answer to Problem 39STP

  $\text{0}\text{.025}$

Explanation of Solution

Given information :

We know that, $6$ new comedy movies, $9$ new family movies, $4$ new drama movies.

Calculation:

  $4$ comedy movies will be chosen in ${}^{\text{6}}{C}_4$ ways and $\text{4}$ poster for family movies can be chosen in ${}^{\text{9}}{C}_4$ ways.

Total ways = ${}^6{C}_4\times {}^9{C}_4$

Total poster = $19$

Required probability = $\frac{{}^6{C}_4\times {}^9{C}_4}{{}^{19}{C}_8}$

  $=\frac{6\times 5}{2}\times \frac{9\times 8\times 7\times 6}{4\times 3\times 2}\times \frac{8\times 7\times 6\times 5\times 4\times 3\times 2}{19\times 18\times 17\times 16\times 15\times 14\times 13\times 12}$

Solving, Probability = $0.025$