Chapter 15.5, Problem 9WE

To determine

To calculate: The number of ways to select three cards from a deck of 52 cards.

Answer to Problem 9WE

The number of ways toselect three cardsare $132600$ .

Explanation of Solution

Given information:

Three cards are drawn one after the other from a deck of 52 cards without replacement.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that three cards are drawn one after the other from a deck of 52 cards without replacement.

Let three cards are $\boxed{}\boxed{}\boxed{}$ .

To select the first card, there are 52 ways $\boxed{52}\boxed{}\boxed{}$ .

Now since one card is out of the deck of cards. Remaining are 51 cards.

To select the second card, there are 51ways $\boxed{52}\boxed{51}\boxed{}$ .

Now since two cards are out of the deck of cards. Remaining are 50 cards.

To select the third card, there are 50ways $\boxed{52}\boxed{51}\boxed{50}$ .

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $52\times 51\times 50=132600$

Thus, the number of ways to select three cards without replacementare $132600$ .