Chapter 8, Problem 8.72RE

(a)

To determine

To calculate the probability that all five cards are diamond.

Answer to Problem 8.72RE

There are $154440$ possibilities.

Explanation of Solution

Use the multiple counting principle and that the fact that there are $13$ diamonds in a deck of cards:

Thus we have,

  $\begin{array}{l}13\times 12\times 11\times 10\times 9\\ =154440\end{array}$

Hence the answer.

(b)

To determine

To calculate the probability of getting a flush.

Answer to Problem 8.72RE

The probability is $0.20\%$ .

Explanation of Solution

There are four suits:

  $\begin{array}{l}154440\times 4\\ =617,760\end{array}$

The number of hands possible are:

  $\begin{array}{l}52\times 51\times 50\times 49\times 48\\ =311,875,200\end{array}$

Therefore, the probability is as:

  $\begin{array}{l}P\text{=}\frac{\text{favorable outcomes}}{\text{possible outcomes}}\\ =\frac{617,760}{311,875,200}\\ =0.0020\\ =0.20\%\end{array}$